Matrix multiplication
In mathematics and linear algebra, matrix multiplication is multiplying two matrices together. The number of columns in the first matrix must be equal to the number of rows in the second matrix. The product of two matrices [math]\displaystyle{ \mathbf{A} }[/math] and [math]\displaystyle{ \mathbf{B} }[/math] is written as [math]\displaystyle{ \mathbf{A}\mathbf{B} }[/math]
To multiply two matrices, the rows of the first matrices are multiplied with the columns of the second. Then, the products are summed to make the entry in the product.
Matrix multiplication is associative, but not commutative.[1]
Matrix Multiplication Media
Matrix multiplication diagram 2
The computation of the bottom left entry of \mathbf{AB} corresponds to the consideration of all paths (highlighted) from basic commodity b_4 to final product f_1 in the production flow graph.
Improvement of estimates of exponent ω over time for the computational complexity of matrix multiplication O(n^\omega).
Related pages
References
- ↑ Weisstein, Eric W. "Matrix Multiplication". mathworld.wolfram.com. Retrieved 23 September 2023.