The specific formula is:

Multiplying determinant with k (constant) = elements of a row or column × k.

Matrix times k (constant) = all elements ×k

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. Because it compactly concentrates a large amount of data, it can sometimes simply represent some complex models.

Extended data:

matrix multiplication

Only when the number of columns in the first matrix A is equal to the number of rows in the other matrix B can the multiplication of two matrices be defined. If a is an m×n matrix and b is an n×p matrix, their product c is an m×p matrix.

, one of its elements:

And write this product as:.

For example:

Matrix multiplication satisfies the following algorithm:

Law of association:?

Left distribution law:?

Law on the distribution of rights:

Matrix multiplication does not satisfy the commutative law.

Matters needing attention in matrix multiplication

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. ..

References:

Baidu encyclopedia-matrix multiplication