# A Summary of Laws of Matrix Operations Often Used in Deep Learning – Deep Learning Tutorial

By | July 23, 2020

Matrix operations are the basic of deep learning, we will list some laws of matrix operations in this tutorial, these laws may help us to simply the computation of formulas.

A, B, C are matrix

(1) A + B = B+ A

(2) A + (B + C) = (A + B) + C

(3) A * (B * C) = (A * B) * C = A * B * C

(4) A * (B + C) = A * B + A * C

(5) (A + B) * C = A * C + B * C

(6) k * (A + B) = k * A + k  *B, k is a scalar

(7) A * I = I * A = A, I is identity matrix

(8) Ap= A*A*A*⋯*A (p factors )

(9) (Ap)*(Aq) = Ap+q

(10) (Ap)q = Apq

(11) AB ≠ BA