### tf.matmul(a, b, transpose_a=False, transpose_b=False, adjoint_a=False, adjoint_b=False, a_is_sparse=False, b_is_sparse=False, name=None)

See the guide: Math > Matrix Math Functions

Multiplies matrix a by matrix b, producing a * b.

The inputs must be matrices (or tensors of rank > 2, representing batches of matrices), with matching inner dimensions, possibly after transposition.

Both matrices must be of the same type. The supported types are: float16, float32, float64, int32, complex64, complex128.

Either matrix can be transposed or adjointed (conjugated and transposed) on the fly by setting one of the corresponding flag to True. These are False by default.

If one or both of the matrices contain a lot of zeros, a more efficient multiplication algorithm can be used by setting the corresponding a_is_sparse or b_is_sparse flag to True. These are False by default. This optimization is only available for plain matrices (rank-2 tensors) with datatypes bfloat16 or float32.

For example:

# 2-D tensor a
a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3]) => [[1. 2. 3.]
[4. 5. 6.]]
# 2-D tensor b
b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2]) => [[7. 8.]
[9. 10.]
[11. 12.]]
c = tf.matmul(a, b) => [[58 64]
[139 154]]

# 3-D tensor a
a = tf.constant(np.arange(1, 13, dtype=np.int32),
shape=[2, 2, 3])                  => [[[ 1.  2.  3.]
[ 4.  5.  6.]],
[[ 7.  8.  9.]
[10. 11. 12.]]]

# 3-D tensor b
b = tf.constant(np.arange(13, 25, dtype=np.int32),
shape=[2, 3, 2])                   => [[[13. 14.]
[15. 16.]
[17. 18.]],
[[19. 20.]
[21. 22.]
[23. 24.]]]
c = tf.matmul(a, b) => [[[ 94 100]
[229 244]],
[[508 532]
[697 730]]]


#### Args:

• a: Tensor of type float16, float32, float64, int32, complex64, complex128 and rank > 1.
• b: Tensor with same type and rank as a.
• transpose_a: If True, a is transposed before multiplication.
• transpose_b: If True, b is transposed before multiplication.
• adjoint_a: If True, a is conjugated and transposed before multiplication.
• adjoint_b: If True, b is conjugated and transposed before multiplication.
• a_is_sparse: If True, a is treated as a sparse matrix.
• b_is_sparse: If True, b is treated as a sparse matrix.
• name: Name for the operation (optional).

#### Returns:

A Tensor of the same type as a and b where each inner-most matrix is the product of the corresponding matrices in a and b, e.g. if all transpose or adjoint attributes are False:

output[..., i, j] = sum_k (a[..., i, k] * b[..., k, j]), for all indices i, j.

• Note: This is matrix product, not element-wise product.

#### Raises:

• ValueError: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True.

Defined in tensorflow/python/ops/math_ops.py.