Matrix Multiplication Calculator
Effortlessly multiply two matrices and visualize the result. Enter your matrices and let's calculate!
Matrix A
Matrix B
Result Matrix (A × B)
Understanding Matrix Multiplication
Matrix multiplication is a fundamental operation in linear algebra, combining two matrices to produce a new matrix. For matrices A (m×n) and B (n×p), their product C (m×p) is calculated by summing the products of elements from the rows of A and columns of B. Specifically, each element Cij is the sum of products of corresponding elements from the i-th row of A and the j-th column of B.
Matrix multiplication is crucial in various fields like computer graphics, physics simulations, and data analysis. It's essential that the number of columns in the first matrix equals the number of rows in the second matrix for the operation to be valid.
For example, if A = [[a, b], [c, d]] and B = [[e, f], [g, h]], then A × B = [[ae+bg, af+bh], [ce+dg, cf+dh]].
Learn more about matrix multiplication on resources like Wikipedia.