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

    a, b, transpose_a=False, transpose_b=False, adjoint_a=False, adjoint_b=False,
    a_is_sparse=False, b_is_sparse=False, name=None

Used in the notebooks

Used in the guide Used in the tutorials

The inputs must, following any transpositions, be tensors of rank >= 2 where the inner 2 dimensions specify valid matrix multiplication dimensions, and any further outer dimensions specify matching batch size.

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.

A simple 2-D tensor matrix multiplication:

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

A batch matrix multiplication with batch shape [2]

a = tf.constant(np.arange(1, 13, dtype=np.int32), shape=[2, 2, 3]) a # 3-D tensor b = tf.constant(np.arange(13, 25, dtype=np.int32), shape=[2, 3, 2]) b # 3-D tensor c = tf.matmul(a, b) c # a * b

Since python >= 3.5 the @ operator is supported (see PEP 465). In TensorFlow, it simply calls the tf.matmul() function, so the following lines are equivalent:

d = a @ b @ [[10], [11]] d = tf.matmul(tf.matmul(a, b), [[10], [11]])


  • a: tf.Tensor of type float16, float32, float64, int32, complex64, complex128 and rank > 1.
  • b: tf.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).


A tf.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.


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