mátrixszorzást

Matrix multiplication is a binary operation that takes two matrices and produces a third matrix. It is a fundamental operation in linear algebra and has numerous applications in mathematics, physics, engineering, and computer science. The product of two matrices A and B is denoted as AB.

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. If A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix. Each element in the resulting matrix is calculated by taking the dot product of the corresponding row from the first matrix and the corresponding column from the second matrix.

Matrix multiplication is associative, meaning that for any three matrices A, B, and C, the equation (AB)C = A(BC) holds. However, it is not commutative, meaning that AB is not necessarily equal to BA.

Matrix multiplication has several properties that make it useful in various applications. For example, it preserves the determinant of a matrix, meaning that det(AB) = det(A)det(B). It also preserves the trace of a matrix, meaning that tr(AB) = tr(BA).

In computer science, matrix multiplication is used in various algorithms, such as the fast Fourier transform and the singular value decomposition. It is also used in graphics and computer vision to perform transformations on objects and images.

In summary, matrix multiplication is a fundamental operation in linear algebra with numerous applications in mathematics, physics, engineering, and computer science. It has several properties that make it useful in various applications, and it is used in various algorithms and transformations.