Lecture 30 linear algebra Lecture 5 eigenvalues and eigenvectors

review

1、 Eigenvalues and eigenvectors

1.1 Definition

1.2 How to find

1.2.1 Concrete matrix

Use trial number method and integral long division method to solve characteristic equation , Find the eigenvalue

1.2.2 Abstract matrix

1.3 nature

2、 be similar

2.1 The matrix is similar

2.1.1 Definition

2.1.2 nature

2.2 Similar diagonalization of matrices

2.2.1 Definition

2.2.2 Conditions for similar diagonalization

2.2.2.1 Two sufficient

2.2.2.2 Two necessities

2.2.3 Similar diagonalization steps

2.3 application

2.3.1 Similar diagonalization of real symmetric matrices

2.3.2 Counter problem

2.3.2.1 Reverse parameter

2.3.2.2 Reverse seeking A

2.3.3 seek A* f(A)