Tensorflow tf.matmul示例不正确？

Question

I read the official document for tf.matmul and I understand the first example. It is a simple [2,3] x [3,2] operation:

a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])

b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])

c = tf.matmul(a, b) => [[58 64]
                    [139 154]]

However, the second example seems very strange :

a = tf.constant(np.arange(1, 13, dtype=np.int32),
            shape=[2, 2, 3])

b = tf.constant(np.arange(13, 25, dtype=np.int32),
            shape=[2, 3, 2])

c = tf.matmul(a, b) => [[[ 94 100]
                     [229 244]],
                    [[508 532]
                     [697 730]]]

Why the matrix with shape [2,2,3] is allowed to multiply with [2,3,2] ?

Answer 1

From the same page ( https://web.archive.org/web/20170223153510/https://www.tensorflow.org/api_docs/python/tf/matmul ):

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 , eg if all transpose or adjoint attributes are False :
output [..., i, j] = sum_k ( a [..., i, k] * b [..., k, j]), for all indices i, j.

Hence a matrix with shape [2,2,3] is allowed to multiply with [2,3,2].