The product of two matrices: https://zh.wikipedia.org/wiki/%E7%9F%A9%E9%99%A3%E4%B9%98%E6%B3%95
In mathematics , matrix multiplication (English: matrix multiplication) is a binary operation that obtains the third matrix based on two matrices . The third matrix is the product of the first two, called matrix product (English: matrix product). Suppose A is an n × m matrix and B is an m × p matrix, then their matrix product AB is an n × p matrix. The m elements in each row in A are multiplied by the corresponding m elements in the corresponding column in B. The sum of these products is an element in AB .
Nature[ edit ]
Matrix multiplication is not commutative (i.e. AB ≠ BA ), except for some special cases more. It is clear to know that it is impossible to expect to get the same result after changing the part of the vector, and the number of columns in the first matrix must be the same as the number of rows in the second matrix. It can also be seen why the matrices are multiplied The order will affect the result.
Although matrix multiplication is not commutative, the determinants of AB and BA will always be the same (when A and B are square matrices of the same size). The explanation is in the determinant entry.