Python and matrix theory--eigenvalues and eigenvectors

Characteristic value knowledge point: "Singular matrix"

• The judgment matrix is not a matrix (the equal number of rows and columns). If the number of rows and columns is not equal, then the singular matrix and the non-singular matrix are not.
  
• Look at the determinant of matrices | a| is equal to 0, if equal to 0, the matrix A is a singular matrix, if not equal to 0, the matrix A is a non-singular matrix.
  

1. If | A|≠0 The matrix A is reversible, the invertible matrix is a non-singular matrix, and the non-singular matrix is also a reversible matrix.
2. If a is singular matrix, then ax=0 has infinite solution, ax=b has infinite solution or no solution.
3. If a is a non-singular matrix, then ax=0 has only a unique zero solution, and Ax=b has a unique solution.

Feature vectorsSummary:
Eigenvalues and eigenvectors: properties of eigenvalues and eigenvalues of eigenvectors: properties of eigenvectors
Example 1 examples 2 Examples 3

Python and matrix theory--eigenvalues and eigenvectors