Answer to Question #109040 in Linear Algebra for Gnanamani CT

Question

Solve the given matrix using strassen’s matrix multiplication
A matrix is 3 5
5 8
B matrix is 8 9
4 7

Answer 1

According to Strassen's algorithm, $\begin{pmatrix} a & b \\c & d\end{pmatrix} \cdot \begin{pmatrix} e & f \\g & h\end{pmatrix} = \begin{pmatrix} p_5 + p_4 - p_2 + p_6 & p_1 + p_2 \\p_3 + p_4 & p_1 + p_5 - p_3 - p_7\end{pmatrix}$, where

$p_1 = a(f-h)\\ p_2 = (a+b)h\\ p_3 = (c+d)e\\ p_4 = d(g-e)$ $p_5 = (a+d)(e+h)\\ p_6 = (b-d)(g+h)\\ p_7 = (a-c)(e+f)$

For our case, $a = 3, b=5, c=5, d=8, e=8, f=9, g=4, h=7$, hence calculating, obtain $p_1 = 6, p_2 = 56, p_3 = 104, p_4 = -32, p_5 = 165, p_6 = -33, p_7 = -34$.

Substituting these parameters into Strassen's formula, obtain $\begin{pmatrix} 44 & 62 \\ 72 & 101\end{pmatrix}$.

The result is easily checked using normal matrix multiplication.