# Module: tf.linalg
Operations for linear algebra. ## Modules [`experimental`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/experimental) module: Public API for tf.linalg.experimental namespace. ## Classes [`class LinearOperator`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperator): Base class defining a \[batch of\] linear operator\[s\]. [`class LinearOperatorAdjoint`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorAdjoint): `LinearOperator` representing the adjoint of another operator. [`class LinearOperatorBlockDiag`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorBlockDiag): Combines one or more `LinearOperators` in to a Block Diagonal matrix. [`class LinearOperatorBlockLowerTriangular`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorBlockLowerTriangular): Combines `LinearOperators` into a blockwise lower-triangular matrix. [`class LinearOperatorCirculant`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorCirculant): `LinearOperator` acting like a circulant matrix. [`class LinearOperatorCirculant2D`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorCirculant2D): `LinearOperator` acting like a block circulant matrix. [`class LinearOperatorCirculant3D`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorCirculant3D): `LinearOperator` acting like a nested block circulant matrix. [`class LinearOperatorComposition`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorComposition): Composes one or more `LinearOperators`. [`class LinearOperatorDiag`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorDiag): `LinearOperator` acting like a \[batch\] square diagonal matrix. [`class LinearOperatorFullMatrix`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorFullMatrix): `LinearOperator` that wraps a \[batch\] matrix. [`class LinearOperatorHouseholder`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorHouseholder): `LinearOperator` acting like a \[batch\] of Householder transformations. [`class LinearOperatorIdentity`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorIdentity): `LinearOperator` acting like a \[batch\] square identity matrix. [`class LinearOperatorInversion`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorInversion): `LinearOperator` representing the inverse of another operator. [`class LinearOperatorKronecker`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorKronecker): Kronecker product between two `LinearOperators`. [`class LinearOperatorLowRankUpdate`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorLowRankUpdate): Perturb a `LinearOperator` with a rank `K` update. [`class LinearOperatorLowerTriangular`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorLowerTriangular): `LinearOperator` acting like a \[batch\] square lower triangular matrix. [`class LinearOperatorPermutation`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorPermutation): `LinearOperator` acting like a \[batch\] of permutation matrices. [`class LinearOperatorScaledIdentity`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorScaledIdentity): `LinearOperator` acting like a scaled \[batch\] identity matrix `A = c I`. [`class LinearOperatorToeplitz`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorToeplitz): `LinearOperator` acting like a \[batch\] of toeplitz matrices. [`class LinearOperatorTridiag`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorTridiag): `LinearOperator` acting like a \[batch\] square tridiagonal matrix. [`class LinearOperatorZeros`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/LinearOperatorZeros): `LinearOperator` acting like a \[batch\] zero matrix. ## Functions [`adjoint(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/adjoint): Transposes the last two dimensions of and conjugates tensor `matrix`. [`band_part(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/band_part): Copy a tensor setting everything outside a central band in each innermost matrix to zero. [`banded_triangular_solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/banded_triangular_solve): Solve triangular systems of equations with a banded solver. [`cholesky(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/cholesky): Computes the Cholesky decomposition of one or more square matrices. [`cholesky_solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/cholesky_solve): Solves systems of linear eqns `A X = RHS`, given Cholesky factorizations. [`cross(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/cross): Compute the pairwise cross product. [`det(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/det): Computes the determinant of one or more square matrices. [`diag(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/diag): Returns a batched diagonal tensor with given batched diagonal values. [`diag_part(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/diag_part): Returns the batched diagonal part of a batched tensor. [`eig(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/eig): Computes the eigen decomposition of a batch of matrices. [`eigh(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/eigh): Computes the eigen decomposition of a batch of self-adjoint matrices. [`eigh_tridiagonal(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/eigh_tridiagonal): Computes the eigenvalues of a Hermitian tridiagonal matrix. [`eigvals(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/eigvals): Computes the eigenvalues of one or more matrices. [`eigvalsh(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/eigvalsh): Computes the eigenvalues of one or more self-adjoint matrices. [`einsum(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/einsum): Tensor contraction over specified indices and outer product. [`expm(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/expm): Computes the matrix exponential of one or more square matrices. [`eye(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/eye): Construct an identity matrix, or a batch of matrices. [`global_norm(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/global_norm): Computes the global norm of multiple tensors. [`inv(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/inv): Computes the inverse of one or more square invertible matrices or their adjoints (conjugate transposes). [`l2_normalize(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/math/l2_normalize): Normalizes along dimension `axis` using an L2 norm. (deprecated arguments) [`logdet(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/logdet): Computes log of the determinant of a hermitian positive definite matrix. [`logm(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/logm): Computes the matrix logarithm of one or more square matrices: [`lstsq(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/lstsq): Solves one or more linear least-squares problems. [`lu(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/lu): Computes the LU decomposition of one or more square matrices. [`lu_matrix_inverse(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/lu_matrix_inverse): Computes the inverse given the LU decomposition(s) of one or more matrices. [`lu_reconstruct(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/lu_reconstruct): The reconstruct one or more matrices from their LU decomposition(s). [`lu_solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/lu_solve): Solves systems of linear eqns `A X = RHS`, given LU factorizations. [`matmul(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/matmul): Multiplies matrix `a` by matrix `b`, producing `a` \* `b`. [`matrix_rank(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/matrix_rank): Compute the matrix rank of one or more matrices. [`matrix_transpose(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/matrix_transpose): Transposes last two dimensions of tensor `a`. [`matvec(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/matvec): Multiplies matrix `a` by vector `b`, producing `a` \* `b`. [`norm(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/norm): Computes the norm of vectors, matrices, and tensors. [`normalize(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/normalize): Normalizes `tensor` along dimension `axis` using specified norm. [`pinv(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/pinv): Compute the Moore-Penrose pseudo-inverse of one or more matrices. [`qr(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/qr): Computes the QR decompositions of one or more matrices. [`set_diag(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/set_diag): Returns a batched matrix tensor with new batched diagonal values. [`slogdet(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/slogdet): Computes the sign and the log of the absolute value of the determinant of [`solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/solve): Solves systems of linear equations. [`sqrtm(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/sqrtm): Computes the matrix square root of one or more square matrices: [`svd(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/svd): Computes the singular value decompositions of one or more matrices. [`tensor_diag(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/tensor_diag): Returns a diagonal tensor with a given diagonal values. [`tensor_diag_part(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/tensor_diag_part): Returns the diagonal part of the tensor. [`tensordot(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/tensordot): Tensor contraction of a and b along specified axes and outer product. [`trace(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/trace): Compute the trace of a tensor `x`. [`triangular_solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/triangular_solve): Solve systems of linear equations with upper or lower triangular matrices. [`tridiagonal_matmul(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/tridiagonal_matmul): Multiplies tridiagonal matrix by matrix. [`tridiagonal_solve(...)`](https://www.tensorflow.org/versions/r2.13/api_docs/python/tf/linalg/tridiagonal_solve): Solves tridiagonal systems of equations.