[Linear algebra] multiplication and Inverse Calculation of Matrices

I. Five Representation Methods of Matrix Multiplication

1. General Form

2. Multiply the matrix and column vector

3. Multiply a matrix and a row vector

4. Multiply Matrix Blocks

Ii. Matrix Inversion

For phalanx, left inverse = Right Inverse

Multiply the original matrix by its inverse matrix to obtain the Unit Matrix
Several methods to determine whether it is reversible:1. the determinant is 02. the columns of the matrix are linear combinations of the columns of the matrix. 3. When the following formula is created, matrix A is irreversible:
Proof:Iii. Matrix Inversion (Gaussian-ruoerdang elimination method) assume that the matrix is:
The metadata elimination process is as follows::

Through the elimination of elements, we convert matrix A to the unit matrix I. At the same time, Matrix I is changed to the inverse matrix of..ProofAs follows:

[Linear algebra] multiplication and Inverse Calculation of Matrices