Name of matrix operation of [ A[0] dot B[0], A[1] dot B[1] ] from 2x2 matrices A, B

Question

Please advise how this matrix operation is called, and what is the numpy operation for it. np.inner, np.dot does not create dot products from 2x2 matrices.

Answer 1

This is the diagonal of the matrix product $AB$, which can be obtained in NumPy using numpy.diagonal and numpy.matmul.

For example

import numpy as np
A = np.matrix('0 1 2; 3 4 5')
B = np.matrix('0 -3; -1 -4; -2 -5');
np.diagonal(np.matmul(A,B)) # or (A*B).diagonal()

yields

array([ -5, -50])

However, this does compute the off-diagonal entries of the matrix product as well and hence isn't very efficient. Describing the entries of your resulting vector as $$ v_i = \sum_j a_{ij} b_{ji} $$ you can obtain the same result more efficiently using numpy.einsum as

np.einsum('ij,ji->i', A, B)