Let λ = 2 be an eigenvalue of invertible matrix A, then matrix (13a) - 1 must have an eigenvalue equal to______ ． | Math enthusiast | Mathematical art

Let λ = 2 be an eigenvalue of invertible matrix A, then matrix (13a) - 1 must have an eigenvalue equal to______ ．

Let α be the eigenvector of the eigenvalue 2 of a, then a α = 2 α and a reversible ∧ α = 2a-1 α, that is, a − 1 α = 12 α ∧ (13a) − 1 α = 3A − 1 α = 32 α ∧ 32 is an eigenvalue of matrix (13a) − 1

RELATED INFORMATIONS

1. There is a m × n matrix A whose rank is n, that is to say, its column vectors are independent. How can we prove that the transpose × a of a is an invertible matrix?
2. Let a be an M × n matrix, C be an invertible matrix of order n, the rank of matrix A is r, and the rank of matrix B = AC is R1, then () A. R ＞ r1b. R ＜ r1c. R = r1d. The relationship between R and R1 depends on C
3. Why is invertible matrix full rank?
4. How to prove that the rank of the sum of two matrices is not less than the sum of matrix ranks rt Hehe, it's the opposite. It should be no more than
5. On the property of matrix rank If a is m × s matrix, B is s × n matrix, if AB = 0, then R (a) + R (b)
6. Properties of matrix rank 4 If P and Q are reversible, then R (PAQ) = R (a)
7. Properties of the rank of linear algebraic matrix If a matrix has a non-zero r-order subformula, and all R + 1-order subformulas containing this r-order subformula are zero, then the rank of the matrix is R. how to prove its correctness or tell me how to deduce from the definition of matrix rank
8. The rank of a is equal to the rank of its transpose matrix. Is this property applicable to any matrix
9. What are the applications of idempotent matrix
10. Let a be a real symmetric idempotent matrix of order n, that is, a & # 178; = a (1) It is proved that there is an orthogonal matrix Q such that (Q-1) AQ = diag (1,1,...) ,1,0,…… ,0） (2) If the rank of a is r, DET (a-2i) is calculated
11. Let the sum of all elements of nonsingular matrix a be 2, then the matrix (1 / 3A ^ 2) ^ - 1 has an eigenvalue equal to () (a) 4 / 3; (b) 3 / 4;
12. Let 2 be an eigenvalue of invertible matrix A, then an eigenvalue of 3A ^ 2 + e is
13. Is the invertibility of (a + b) matrix equal to the invertibility of a + if not, what
14. How to prove that matrix A is invertible if and only if 0 is not the eigenvalue of a GOT IT
15. It is proved that the necessary and sufficient condition of invertibility of matrix A is that its eigenvalues are not equal to zero
16. Let the eigenvalues of the third order invertible matrix a be 1, 2 and 4 respectively, then [i-2a ^ - 1] is equal to It's the value of the determinant,
17. Linear Algebra: there is a problem -- let a = (1,0, - 1) t, matrix A = AAT, n be a positive integer, find the determinant of ae-a ^ n? There is a sentence in the answer: from R (a) = 1, we know that the eigenvalues of a are 2,0,0?
18. Let | a | = D ≠ 0 be the determinant of matrix A of order n, and find | a*| Adjoint matrix of a
19. If matrix a satisfies: AAT = E and | a | = - 1, then matrix a must have an eigenvalue of - 1. Why is it equal to proving that the determinant of | a + e | is 0
20. The rank of matrix A is 1. It is proved that the eigenvalue of a has n-1 zeros? The rank of matrix A is 1. It is proved that the eigenvalue of a has n-1 zeros and another eigenvalue is the sum of diagonal elements Would you like to be more detailed? What does this diagram show?