mátrixszorozáshoz

Mátrixszorzás is the Hungarian term for matrix multiplication. It is a fundamental operation in linear algebra that takes two matrices and produces a new matrix. For the multiplication of matrix A by matrix B to be defined, the number of columns in matrix A must be equal to the number of rows in matrix B. If matrix A has dimensions m x n and matrix B has dimensions n x p, the resulting matrix C will have dimensions m x p.

The element in the i-th row and j-th column 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 involves multiplying corresponding elements of the row and column and summing these products. For example, if A is a 2x3 matrix and B is a 3x2 matrix, the resulting matrix C will be a 2x2 matrix. Each element of C is the sum of three products.

Matrix multiplication is not commutative, meaning that in general, A * B is not equal to B * A. However, it is associative, so (A * B) * C = A * (B * C). This operation is widely used in various fields, including computer graphics, physics, engineering, and machine learning, for tasks such as transformations, solving systems of linear equations, and data analysis. Efficient algorithms exist for performing matrix multiplication, especially for large matrices, as its computational cost can be significant.