Law of multiplicative association: (ab) c = a (BC); Multiplication left distribution law: (a+b) c = AC+BC;

Right distribution law of multiplication: c (a+b) = ca+CB; The associative law of logarithmic multiplication k(AB)=(kA)B=A(kB).

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. The matrix of m×n is a digital array in which m×n numbers are arranged in m rows and n columns.

Related concepts of matrix:

1, row matrix, column matrix: in m×n matrix, m= 1, which is called row matrix, also called n-dimensional row vector; N= 1, called column matrix, also called m-dimensional column vector.

2. Zero matrix: m×n matrix with all elements of 0.

3.n-order square matrix: in m×n-order matrix A, m = n；; N-order square matrix A, determinant can be defined as | A |n-order square matrix has main diagonal and main diagonal elements.

4. identity matrix: An N-order square with all the elements on the main diagonal being 1 and all the other elements being 0 is called an N-order identity matrix, and is denoted as E. ..

5. Diagonal matrix: An N-order square matrix with all elements on the non-main diagonal is called a diagonal matrix.

6. Quantity matrix: When the elements on the main diagonal of the N-order diagonal matrix are equal, it is called quantity matrix.

7. Upper (lower) triangular matrix: in an n-order square matrix, all the elements below the main diagonal are zero, which is called the upper triangular matrix; All the elements above the main diagonal are zero, which is called the lower triangular matrix.