Created At: [[2025-02-18]] # Algorithms and Matrix Multiplication Below is my notes, or rather my attempt to practice the Feynman Technique in my readings of two wonderfully difficult books: - *Probability and Computing (Second Edition)* by Mitzenmacher and Upfal - *Introduction to Algorithms (Fourth Edition)* by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford STEIN. ## 1. Basic Matrix Multiplications Say that we have two matrices $A$ and $B$ each of rank $2$ defined as follows: $ A := \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix},\quad \text{and}\quad B := \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix}. $