Mátrixszorzás

Matrix multiplication is a binary operation that takes two matrices and produces a third matrix. It is defined only for matrices where the number of columns in the first matrix is equal to the number of rows in the second matrix. The resulting matrix, known as the product matrix, has the same number of rows as the first matrix and the same number of columns as the second matrix.

The element in the i-th row and j-th column of the product matrix is obtained by multiplying the elements of the i-th row of the first matrix by the corresponding elements of the j-th column of the second matrix, then summing these products. This process is repeated for each element in the product matrix.

Matrix multiplication is not commutative, meaning that AB is not necessarily equal to BA. It is also not generally associative, although it is associative for square matrices of the same size.

Matrix multiplication has numerous applications in mathematics, physics, engineering, and computer science. It is used in solving systems of linear equations, in the study of linear transformations, and in the design of algorithms for data processing and analysis.