If a, b and c represent three matrices with C=AB, a is n rows and m columns, and b is m rows and q columns, then c is n rows and q columns.

Then cij = ai1* b1j+ai2 * b2j+ai3 * b3j+...+ain * bnj for any element of the c matrix.

The most important method of matrix multiplication is generalized matrix product. It only makes sense when the number of columns in the first matrix is the same as the number of rows in the second matrix. When we generally refer to matrix product, we mean general matrix product.

1. When the number of columns of matrix A is equal to the number of rows of matrix B, A and B can be multiplied.

2. The number of rows of matrix C is equal to that of matrix A, and the number of columns of matrix C is equal to that of matrix B. ..

3. The elements in row M and column N of product C are equal to the sum of the products of the elements in row M of matrix A and the corresponding elements in column N of matrix B. ..

Operation rules of matrix multiplication:

Suddenly, the operation rules of matrix multiplication were born. Perhaps Gloria is particularly lucky, perhaps his mathematical intuition is particularly keen, but in any case, he gave a natural and useful definition of matrix multiplication.

Gloria's basic idea is to represent linear composite mapping by matrix product, but he is not the first mathematician to consider linear composite mapping. As early as 180 1 year, C.F.Gauss used this compound calculation, but Gauss did not record the coefficients in the form of an array.