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Matrix Multiplication

May 09, 20242 min read

Types: Not Applicable
Examples: Not Applicable
Constructions: Not Applicable
Generalizations: Not Applicable

Properties: Noncommutativity of Matrix Multiplication, The ith Column of A is Aei, The ith Column of AB is Abi, The ith Row of AB is the Product of The ith Row of A and Matrix B, Matrix Multiplication is Associative
Sufficiencies: Not Applicable
Equivalences: Not Applicable
Justifications: Not Applicable

Matrix Multiplication

If is an Matrix whose th entry is and is an matrix whose th entry is , then is the matrix with entries

Example:

Misplaced &2 & 3\end{bmatrix}\begin{bmatrix}0 & 1 \\ 0 & 1\end{bmatrix}=\begin{bmatrix}1(0)+0(0) & 1(1)+0(1) \\ 2(0)+3(0) & 2(1)+3(1)\end{bmatrix}=\begin{bmatrix}0 & 1 \\ 0 & 5\end{bmatrix}$$

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