It is known that the fourth-order square matrix a satisfies | A-E | = 0, square matrix B = a ^ 3-3a ^ 2, BB ^ t = 2E, and | B|

It is known that the fourth-order square matrix a satisfies | A-E | = 0, square matrix B = a ^ 3-3a ^ 2, BB ^ t = 2E, and | B|

Given the matrix M = 2321, find the eigenvalues and eigenvectors of matrix M. test point: the calculation of eigenvalues and eigenvectors. Special topic: calculation problem. Analysis: first, list the characteristic polynomials according to the definition of eigenvalues, Let f (λ) = 0, solve the equation to get the eigenvalues, and then list the equations from the eigenvalues to get the corresponding eigenvectors

Let the eigenvalues of a square matrix of order 3 be 1, - 1,2, and find | a * + 3a-2e |

If the eigenvalue of a is x0, then the eigenvalue of a * is | a | / x0
In addition, note that the determinant of a square matrix is the product of all eigenvalues
If the calculation is correct, it should be = 9

Let the eigenvalue of a matrix of order 3 be - 1, 2 - 3, then the eigenvalue of a 'is -

The determinant of a * = a multiplied by the inverse of a = (- 1 multiplied by 2 multiplied by - 3) multiplied by the inverse of a = 6 times the inverse of a, the eigenvalue of a is - 1, 2 - 3, the eigenvalue of a is - 1, 1 / 2, - 1 / 3, so the eigenvalue of a * is - 6, 3, - 2