Current location - Training Enrollment Network - Mathematics courses - Postgraduate entrance examination, advanced mathematics, linear algebra, how did he write this solution? Just like Li Yongle, the second teacher, didn't say it in class, not the unit time.
Postgraduate entrance examination, advanced mathematics, linear algebra, how did he write this solution? Just like Li Yongle, the second teacher, didn't say it in class, not the unit time.
Learning point

If the eigenvalue of matrix A is λ 1, λ2, ..., λn, then | a | = λ1λ 2 ... λ n.

explain

|A|= 1×2×...×n= n!

Let the eigenvalue of A be λ and the eigenvector of A be α.

Then Aα = λα

So (a? -A)α = A? α - Aα = λ? α - λα = (λ? -λ)α

So a? The eigenvalue of -A is λ? -λ, and the corresponding feature vector is α.

Answer? The eigenvalue of -A is 0, 2, 6, ..., n? Tong -EN

To annotate ...

For a polynomial, its eigenvalue is the corresponding characteristic polynomial.

Linear algebra includes determinant, matrix, linear equations, vector space and linear transformation, eigenvalue and eigenvector, matrix diagonalization, quadratic form and its application.