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.