Mátrixszorzat

Mátrixszorzat is the Hungarian term for matrix multiplication. It is a binary operation that produces a new matrix from two matrices. The number of columns in the first matrix must be equal to the number of rows in the second matrix for the multiplication to be defined. If matrix A has dimensions m x n and matrix B has dimensions n x p, then their product, matrix C, will have dimensions m x p.

The element at row i and column j of the resulting matrix C is calculated by taking the dot product of the i-th row of matrix A and the j-th column of matrix B. This means summing the products of corresponding elements from the row and column. For example, if A is a 2x3 matrix and B is a 3x2 matrix, the resulting matrix C will be 2x2. Each element of C is found by multiplying a row of A with a column of B.

Matrix multiplication is not commutative, meaning that in general, A * B is not equal to B * A. It is, however, associative, meaning (A * B) * C = A * (B * C), and distributive, meaning A * (B + C) = A * B + A * C. This operation is fundamental in linear algebra and has widespread applications in fields such as computer graphics, physics, engineering, and data science. It is used to represent linear transformations, solve systems of linear equations, and perform various calculations in computational models.