Matrix Multiplication
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Matrix Multiplication
Resultant Matrix
Matrix multiplication is not commutative (A × B ≠ B × A). It involves taking the dot product of rows from the first matrix and columns from the second.
How it Works
Matrix multiplication is not as simple as multiplying corresponding numbers. Instead, it involves the dot product of rows and columns.
The Dot Product Rule
The entry in the first row and first column of the result is the dot product of the first row of A and the first column of B.
(a11 × b11) + (a12 × b21)Key Properties
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Non-Commutative
In most cases, AB is not equal to BA. Order matters significantly in matrix multiplication.
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Associative
The property (AB)C = A(BC) does hold true for matrices.
"Matrix multiplication is the language of transformations. Every 3D rotation or scale in your favorite video game is a matrix multiplication."