Matrix multiplication

Matrix multiplication of matrices A and B is a third matrix, C:

C = AB

The element-wise product of matrices is called a Hadamard product and is denoted as A.B.

The dot product of two vectors x and y of the same dimensionality is the matrix product x transposing y. Matrix product C = AB is like computing C_i,j as the dot product between row i of matrix A and column j of matrix B:

The following example shows the Hadamard product and dot product using tensor objects:

import tensorflow as tf
 
mat1 = tf.constant([[4, 5, 6],[3,2,1]])
mat2 = tf.constant([[7, 8, 9],[10, 11, 12]])
 
# hadamard product (element wise)
mult = tf.multiply(mat1, mat2)
 
# dot product (no. of rows = no. of columns)
dotprod = tf.matmul(mat1, tf.transpose(mat2))
 
with tf.Session() as sess:
    print(sess.run(mult))
    print(sess.run(dotprod))

The output of the listing is shown as follows:

[[28 40 54][30 22 12]]
 [[122 167][ 46 64]]