# tf.linalg.LinearOperator

<br />

|---|
| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L90-L1281) |

Base class defining a \[batch of\] linear operator\[s\].

Inherits From: [`Module`](https://www.tensorflow.org/versions/r2.14/api_docs/python/tf/Module)

#### View aliases


**Compat aliases for migration**

See
[Migration guide](https://www.tensorflow.org/guide/migrate) for
more details.

[`tf.compat.v1.linalg.LinearOperator`](https://www.tensorflow.org/api_docs/python/tf/linalg/LinearOperator)

<br />

    tf.linalg.LinearOperator(
        dtype,
        graph_parents=None,
        is_non_singular=None,
        is_self_adjoint=None,
        is_positive_definite=None,
        is_square=None,
        name=None,
        parameters=None
    )

Subclasses of `LinearOperator` provide access to common methods on a
(batch) matrix, without the need to materialize the matrix. This allows:

- Matrix free computations
- Operators that take advantage of special structure, while providing a consistent API to users.

#### Subclassing

To enable a public method, subclasses should implement the leading-underscore
version of the method. The argument signature should be identical except for
the omission of `name="..."`. For example, to enable
`matmul(x, adjoint=False, name="matmul")` a subclass should implement
`_matmul(x, adjoint=False)`.

#### Performance contract

Subclasses should only implement the assert methods
(e.g. `assert_non_singular`) if they can be done in less than `O(N^3)`
time.

Class docstrings should contain an explanation of computational complexity.
Since this is a high-performance library, attention should be paid to detail,
and explanations can include constants as well as Big-O notation.

#### Shape compatibility

`LinearOperator` subclasses should operate on a \[batch\] matrix with
compatible shape. Class docstrings should define what is meant by compatible
shape. Some subclasses may not support batching.

#### Examples:

`x` is a batch matrix with compatible shape for `matmul` if

    operator.shape = [B1,...,Bb] + [M, N],  b >= 0,
    x.shape =   [B1,...,Bb] + [N, R]

`rhs` is a batch matrix with compatible shape for `solve` if

    operator.shape = [B1,...,Bb] + [M, N],  b >= 0,
    rhs.shape =   [B1,...,Bb] + [M, R]

#### Example docstring for subclasses.

This operator acts like a (batch) matrix `A` with shape
`[B1,...,Bb, M, N]` for some `b >= 0`. The first `b` indices index a
batch member. For every batch index `(i1,...,ib)`, `A[i1,...,ib, : :]` is
an `m x n` matrix. Again, this matrix `A` may not be materialized, but for
purposes of identifying and working with compatible arguments the shape is
relevant.

#### Examples:

    some_tensor = ... shape = ????
    operator = MyLinOp(some_tensor)

    operator.shape()
    ==> [2, 4, 4]

    operator.log_abs_determinant()
    ==> Shape [2] Tensor

    x = ... Shape [2, 4, 5] Tensor

    operator.matmul(x)
    ==> Shape [2, 4, 5] Tensor

#### Shape compatibility

This operator acts on batch matrices with compatible shape.
FILL IN WHAT IS MEANT BY COMPATIBLE SHAPE

#### Performance

FILL THIS IN

#### Matrix property hints

This `LinearOperator` is initialized with boolean flags of the form `is_X`,
for `X = non_singular, self_adjoint, positive_definite, square`.
These have the following meaning:

- If `is_X == True`, callers should expect the operator to have the property `X`. This is a promise that should be fulfilled, but is *not* a runtime assert. For example, finite floating point precision may result in these promises being violated.
- If `is_X == False`, callers should expect the operator to not have `X`.
- If `is_X == None` (the default), callers should have no expectation either way.

#### Initialization parameters

All subclasses of `LinearOperator` are expected to pass a `parameters`
argument to `super().__init__()`. This should be a `dict` containing
the unadulterated arguments passed to the subclass `__init__`. For example,
`MyLinearOperator` with an initializer should look like:

    def __init__(self, operator, is_square=False, name=None):
       parameters = dict(
           operator=operator,
           is_square=is_square,
           name=name
       )
       ...
       super().__init__(..., parameters=parameters)

Users can then access `my_linear_operator.parameters` to see all arguments
passed to its initializer.

<br />

<br />

<br />

| ## Args ||
|---|---|
| `dtype` | The type of the this `LinearOperator`. Arguments to `matmul` and `solve` will have to be this type. |
| `graph_parents` | (Deprecated) Python list of graph prerequisites of this `LinearOperator` Typically tensors that are passed during initialization |
| `is_non_singular` | Expect that this operator is non-singular. |
| `is_self_adjoint` | Expect that this operator is equal to its hermitian transpose. If `dtype` is real, this is equivalent to being symmetric. |
| `is_positive_definite` | Expect that this operator is positive definite, meaning the quadratic form `x^H A x` has positive real part for all nonzero `x`. Note that we do not require the operator to be self-adjoint to be positive-definite. See: https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices |
| `is_square` | Expect that this operator acts like square \[batch\] matrices. |
| `name` | A name for this `LinearOperator`. |
| `parameters` | Python `dict` of parameters used to instantiate this `LinearOperator`. |

<br />

<br />

<br />

<br />

| ## Raises ||
|---|---|
| `ValueError` | If any member of graph_parents is `None` or not a `Tensor`. |
| `ValueError` | If hints are set incorrectly. |

<br />

<br />

<br />

<br />

| ## Attributes ||
|---|---|
| `H` | Returns the adjoint of the current `LinearOperator`. <br /> Given `A` representing this `LinearOperator`, return `A*`. Note that calling `self.adjoint()` and `self.H` are equivalent. |
| `batch_shape` | `TensorShape` of batch dimensions of this `LinearOperator`. <br /> If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb])`, equivalent to `A.shape[:-2]` |
| `domain_dimension` | Dimension (in the sense of vector spaces) of the domain of this operator. <br /> If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `N`. |
| `dtype` | The `DType` of `Tensor`s handled by this `LinearOperator`. |
| `graph_parents` | List of graph dependencies of this `LinearOperator`. (deprecated) <br /> > [!WARNING] > **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Do not call `graph_parents`. |
| `is_non_singular` | <br /> |
| `is_positive_definite` | <br /> <br /> |
| `is_self_adjoint` | <br /> <br /> |
| `is_square` | Return `True/False` depending on if this operator is square. |
| `parameters` | Dictionary of parameters used to instantiate this `LinearOperator`. |
| `range_dimension` | Dimension (in the sense of vector spaces) of the range of this operator. <br /> If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `M`. |
| `shape` | `TensorShape` of this `LinearOperator`. <br /> If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb, M, N])`, equivalent to `A.shape`. |
| `tensor_rank` | Rank (in the sense of tensors) of matrix corresponding to this operator. <br /> If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `b + 2`. |

<br />

## Methods

### `add_to_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1125-L1138)

    add_to_tensor(
        x, name='add_to_tensor'
    )

Add matrix represented by this operator to `x`. Equivalent to `A + x`.

<br />

<br />

<br />

| Args ||
|---|---|
| `x` | `Tensor` with same `dtype` and shape broadcastable to `self.shape`. |
| `name` | A name to give this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| A `Tensor` with broadcast shape and same `dtype` as `self`. ||

<br />

### `adjoint`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L981-L996)

    adjoint(
        name='adjoint'
    )

Returns the adjoint of the current `LinearOperator`.

Given `A` representing this `LinearOperator`, return `A*`.
Note that calling `self.adjoint()` and `self.H` are equivalent.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `LinearOperator` which represents the adjoint of this `LinearOperator`. ||

<br />

### `assert_non_singular`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L585-L603)

    assert_non_singular(
        name='assert_non_singular'
    )

Returns an `Op` that asserts this operator is non singular.

This operator is considered non-singular if

    ConditionNumber < max{100, range_dimension, domain_dimension} * eps,
    eps := np.finfo(self.dtype.as_numpy_dtype).eps

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A string name to prepend to created ops. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is singular. ||

<br />

### `assert_positive_definite`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L621-L636)

    assert_positive_definite(
        name='assert_positive_definite'
    )

Returns an `Op` that asserts this operator is positive definite.

Here, positive definite means that the quadratic form `x^H A x` has positive
real part for all nonzero `x`. Note that we do not require the operator to
be self-adjoint to be positive definite.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name to give this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is not positive definite. ||

<br />

### `assert_self_adjoint`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L648-L662)

    assert_self_adjoint(
        name='assert_self_adjoint'
    )

Returns an `Op` that asserts this operator is self-adjoint.

Here we check that this operator is *exactly* equal to its hermitian
transpose.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A string name to prepend to created ops. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is not self-adjoint. ||

<br />

### `batch_shape_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L397-L412)

    batch_shape_tensor(
        name='batch_shape_tensor'
    )

Shape of batch dimensions of this operator, determined at runtime.

If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb]`.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `int32` `Tensor` ||

<br />

### `cholesky`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1026-L1049)

    cholesky(
        name='cholesky'
    )

Returns a Cholesky factor as a `LinearOperator`.

Given `A` representing this `LinearOperator`, if `A` is positive definite
self-adjoint, return `L`, where `A = L L^T`, i.e. the cholesky
decomposition.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `LinearOperator` which represents the lower triangular matrix in the Cholesky decomposition. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `ValueError` | When the `LinearOperator` is not hinted to be positive definite and self adjoint. |

<br />

### `cond`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1175-L1185)

    cond(
        name='cond'
    )

Returns the condition number of this linear operator.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| Shape `[B1,...,Bb]` `Tensor` of same `dtype` as `self`. ||

<br />

### `determinant`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L781-L798)

    determinant(
        name='det'
    )

Determinant for every batch member.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `Tensor` with shape `self.batch_shape` and same `dtype` as `self`. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `NotImplementedError` | If `self.is_square` is `False`. |

<br />

### `diag_part`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1076-L1102)

    diag_part(
        name='diag_part'
    )

Efficiently get the \[batch\] diagonal part of this operator.

If this operator has shape `[B1,...,Bb, M, N]`, this returns a
`Tensor` `diagonal`, of shape `[B1,...,Bb, min(M, N)]`, where
`diagonal[b1,...,bb, i] = self.to_dense()[b1,...,bb, i, i]`.

    my_operator = LinearOperatorDiag([1., 2.])

    # Efficiently get the diagonal
    my_operator.diag_part()
    ==> [1., 2.]

    # Equivalent, but inefficient method
    tf.linalg.diag_part(my_operator.to_dense())
    ==> [1., 2.]

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `diag_part` | A `Tensor` of same `dtype` as self. |

<br />

### `domain_dimension_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L484-L500)

    domain_dimension_tensor(
        name='domain_dimension_tensor'
    )

Dimension (in the sense of vector spaces) of the domain of this operator.

Determined at runtime.

If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `N`.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `int32` `Tensor` ||

<br />

### `eigvals`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1143-L1160)

    eigvals(
        name='eigvals'
    )

Returns the eigenvalues of this linear operator.

If the operator is marked as self-adjoint (via `is_self_adjoint`)
this computation can be more efficient.

> [!NOTE]
> **Note:** This currently only supports self-adjoint operators.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| Shape `[B1,...,Bb, N]` `Tensor` of same `dtype` as `self`. ||

<br />

### `inverse`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1001-L1024)

    inverse(
        name='inverse'
    )

Returns the Inverse of this `LinearOperator`.

Given `A` representing this `LinearOperator`, return a `LinearOperator`
representing `A^-1`.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name scope to use for ops added by this method. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `LinearOperator` representing inverse of this matrix. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `ValueError` | When the `LinearOperator` is not hinted to be `non_singular`. |

<br />

### `log_abs_determinant`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L810-L827)

    log_abs_determinant(
        name='log_abs_det'
    )

Log absolute value of determinant for every batch member.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `Tensor` with shape `self.batch_shape` and same `dtype` as `self`. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `NotImplementedError` | If `self.is_square` is `False`. |

<br />

### `matmul`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L675-L728)

    matmul(
        x, adjoint=False, adjoint_arg=False, name='matmul'
    )

Transform \[batch\] matrix `x` with left multiplication: `x --> Ax`.

    # Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
    operator = LinearOperator(...)
    operator.shape = [..., M, N]

    X = ... # shape [..., N, R], batch matrix, R > 0.

    Y = operator.matmul(X)
    Y.shape
    ==> [..., M, R]

    Y[..., :, r] = sum_j A[..., :, j] X[j, r]

<br />

<br />

<br />

| Args ||
|---|---|
| `x` | `LinearOperator` or `Tensor` with compatible shape and same `dtype` as `self`. See class docstring for definition of compatibility. |
| `adjoint` | Python `bool`. If `True`, left multiply by the adjoint: `A^H x`. |
| `adjoint_arg` | Python `bool`. If `True`, compute `A x^H` where `x^H` is the hermitian transpose (transposition and complex conjugation). |
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| A `LinearOperator` or `Tensor` with shape `[..., M, R]` and same `dtype` as `self`. ||

<br />

### `matvec`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L738-L771)

    matvec(
        x, adjoint=False, name='matvec'
    )

Transform \[batch\] vector `x` with left multiplication: `x --> Ax`.

    # Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
    operator = LinearOperator(...)

    X = ... # shape [..., N], batch vector

    Y = operator.matvec(X)
    Y.shape
    ==> [..., M]

    Y[..., :] = sum_j A[..., :, j] X[..., j]

<br />

<br />

<br />

| Args ||
|---|---|
| `x` | `Tensor` with compatible shape and same `dtype` as `self`. `x` is treated as a \[batch\] vector meaning for every set of leading dimensions, the last dimension defines a vector. See class docstring for definition of compatibility. |
| `adjoint` | Python `bool`. If `True`, left multiply by the adjoint: `A^H x`. |
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| A `Tensor` with shape `[..., M]` and same `dtype` as `self`. ||

<br />

### `range_dimension_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L528-L544)

    range_dimension_tensor(
        name='range_dimension_tensor'
    )

Dimension (in the sense of vector spaces) of the range of this operator.

Determined at runtime.

If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `M`.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `int32` `Tensor` ||

<br />

### `shape_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L363-L381)

    shape_tensor(
        name='shape_tensor'
    )

Shape of this `LinearOperator`, determined at runtime.

If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb, M, N]`, equivalent to [`tf.shape(A)`](https://www.tensorflow.org/versions/r2.14/api_docs/python/tf/shape).

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `int32` `Tensor` ||

<br />

### `solve`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L848-L923)

    solve(
        rhs, adjoint=False, adjoint_arg=False, name='solve'
    )

Solve (exact or approx) `R` (batch) systems of equations: `A X = rhs`.

The returned `Tensor` will be close to an exact solution if `A` is well
conditioned. Otherwise closeness will vary. See class docstring for details.

#### Examples:

    # Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
    operator = LinearOperator(...)
    operator.shape = [..., M, N]

    # Solve R > 0 linear systems for every member of the batch.
    RHS = ... # shape [..., M, R]

    X = operator.solve(RHS)
    # X[..., :, r] is the solution to the r'th linear system
    # sum_j A[..., :, j] X[..., j, r] = RHS[..., :, r]

    operator.matmul(X)
    ==> RHS

<br />

<br />

<br />

| Args ||
|---|---|
| `rhs` | `Tensor` with same `dtype` as this operator and compatible shape. `rhs` is treated like a \[batch\] matrix meaning for every set of leading dimensions, the last two dimensions defines a matrix. See class docstring for definition of compatibility. |
| `adjoint` | Python `bool`. If `True`, solve the system involving the adjoint of this `LinearOperator`: `A^H X = rhs`. |
| `adjoint_arg` | Python `bool`. If `True`, solve `A X = rhs^H` where `rhs^H` is the hermitian transpose (transposition and complex conjugation). |
| `name` | A name scope to use for ops added by this method. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `Tensor` with shape `[...,N, R]` and same `dtype` as `rhs`. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `NotImplementedError` | If `self.is_non_singular` or `is_square` is False. |

<br />

### `solvevec`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L931-L979)

    solvevec(
        rhs, adjoint=False, name='solve'
    )

Solve single equation with best effort: `A X = rhs`.

The returned `Tensor` will be close to an exact solution if `A` is well
conditioned. Otherwise closeness will vary. See class docstring for details.

#### Examples:

    # Make an operator acting like batch matrix A.  Assume A.shape = [..., M, N]
    operator = LinearOperator(...)
    operator.shape = [..., M, N]

    # Solve one linear system for every member of the batch.
    RHS = ... # shape [..., M]

    X = operator.solvevec(RHS)
    # X is the solution to the linear system
    # sum_j A[..., :, j] X[..., j] = RHS[..., :]

    operator.matvec(X)
    ==> RHS

<br />

<br />

<br />

| Args ||
|---|---|
| `rhs` | `Tensor` with same `dtype` as this operator. `rhs` is treated like a \[batch\] vector meaning for every set of leading dimensions, the last dimension defines a vector. See class docstring for definition of compatibility regarding batch dimensions. |
| `adjoint` | Python `bool`. If `True`, solve the system involving the adjoint of this `LinearOperator`: `A^H X = rhs`. |
| `name` | A name scope to use for ops added by this method. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `Tensor` with shape `[...,N]` and same `dtype` as `rhs`. ||

<br />

<br />

<br />

<br />

| Raises ||
|---|---|
| `NotImplementedError` | If `self.is_non_singular` or `is_square` is False. |

<br />

### `tensor_rank_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L441-L455)

    tensor_rank_tensor(
        name='tensor_rank_tensor'
    )

Rank (in the sense of tensors) of matrix corresponding to this operator.

If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `b + 2`.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| `int32` `Tensor`, determined at runtime. ||

<br />

### `to_dense`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1067-L1070)

    to_dense(
        name='to_dense'
    )

Return a dense (batch) matrix representing this operator.

### `trace`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1107-L1119)

    trace(
        name='trace'
    )

Trace of the linear operator, equal to sum of `self.diag_part()`.

If the operator is square, this is also the sum of the eigenvalues.

<br />

<br />

<br />

| Args ||
|---|---|
| `name` | A name for this `Op`. |

<br />

<br />

<br />

<br />

| Returns ||
|---|---|
| Shape `[B1,...,Bb]` `Tensor` of same `dtype` as `self`. ||

<br />

### `__getitem__`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L1262-L1263)

    __getitem__(
        slices
    )

### `__matmul__`

[View source](https://github.com/tensorflow/tensorflow/blob/v2.14.0/tensorflow/python/ops/linalg/linear_operator.py#L730-L731)

    __matmul__(
        other
    )