Multiplication of Matrices

==2024-11-20

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Theory

Set for Matrix Multiplication

Matrix Multiplication is defined for $M_{m\times n}(\mathbb{F}(\mathbb{R}/\mathbb{C},+,.))$.

Consider 2 matrices $A_{m\times p}$ , $B_{p\times n}$. Then, $C=AB$ exists of order $m\times n$ such that,

$C=AB=[c_{ij}{]}_{m\times n}$

where,

$$c_{ij}=\sum _{k=1}^p(a_{ik}{b}_{kj})$$

where, $i\in [1,m]\text{ and }j\in [1,n]$

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Implementation

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PTR