Excuse me, are two matrices equivalent? Are the values of their determinants equal?
If there are invertible matrices P and Q such that PAQ = B, then a and B are equivalent
Here, the determinants of P and Q are not required, so the determinants of a and B are not necessarily equal
RELATED INFORMATIONS
- 1. The matrix A and B are equivalent. Find out whether the determinants of a and B are equal
- 2. Let a be a matrix of order m * n, and the rank of a is equal to m and less than N. why is the determinant of (transpose of a multiplied by a) equal to zero
- 3. Let a be an M * n matrix and B be an n * m matrix. It is proved that when m > N, there must be | ab | = 0
- 4. If a matrix is not a square matrix, but its row full rank or column full rank, then the determinant value of the matrix must not be 0?
- 5. Let the eigenvalues of a matrix of order 3 be different from each other. If the determinant is used, then the rank of a is
- 6. Is there any relation between the value of determinant and the invertibility of matrix in linear algebra?
- 7. Is the value of the determinant of the inverse matrix consistent with the original matrix?
- 8. Will the rank of transpose matrix change compared with the original matrix
- 9. Let a be an invertible real matrix of order. It is proved that there exists a positive definite symmetric matrix s and an orthogonal matrix U such that
- 10. 1、1、2、3、5、8、13…… . 90 numbers in a row, then, what is the remainder of the sum of these 90 numbers divided by 5
- 11. A square matrix of order n is similar to a diagonal matrix A. the order of a square matrix A is equal to N, right
- 12. A. B is a square matrix of order n. It is proved that AB and Ba have the same eigenvalues
- 13. Let the eigenvalues of a square matrix of order 3 be 1,2,0, and its corresponding eigenvectors A1, A2, A3. B = a ^ 3-2a + 3E, and find the eigenvector of B ^ - 1 Why A1, A2, A3? It's not mentioned in the book. What's the basis
- 14. If we know that the fourth-order square matrix A is similar to B, and the eigenvalues of a are 2,3,4,5, then | B-I | =? (where I is the fourth-order identity matrix) Why is the eigenvalue of B-I 2-1,3-1,4-1,5-1, that is: 1,2,3,4
- 15. Let n-order real square matrix A = a ^ 2 and E be n-order identity matrix. It is proved that R (a) + R (A-E) = n
- 16. Let n-order square matrix a satisfy a * A-A + e = 0, and prove that a is an invertible matrix
- 17. If a is a square matrix of order n, e is a unit matrix of order n, and a ^ 3 = O, it is proved that A-E is an invertible matrix!
- 18. Given that the eigenvalues of matrix A of order 3 are 1,2,3, try to find the eigenvalues of B = 1 / 2A * + 3E
- 19. Let n-order matrix a satisfy a ^ 2 + 2A – 3E = 0, prove that a + 4E is invertible, and find their inverse
- 20. Let square matrix a satisfy a ^ 2-2a + 4E = O, prove that a + E and a-3e are invertible, and find their inverse matrix I know how to do it, but I don't understand why. Could you please explain how to do it? That is, list the process and explain each step. Thank you!