The rank of a is equal to the rank of its transpose matrix. Is this property applicable to any matrix
It can be applied to any one of them
Because the row rank of a is equal to the column rank of a transpose, the row rank and column rank of a matrix are equal
RELATED INFORMATIONS
- 1. What are the applications of idempotent matrix
- 2. 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
- 3. What is a positive definite matrix? What are the properties of a positive definite matrix? If a is a positive definite matrix, then a [i] [i] must be greater than 0?
- 4. Is the row rank of a matrix always equal to the column rank and equal to the rank of a matrix? Another problem is that if a matrix A is m rows and N columns, and M
- 5. The rank of the sum of two matrices is less than or equal to the sum of the ranks of two matrices? How to prove
- 6. Excuse me, teacher, why is "the rank of a matrix equal to the rank of its column vector group, and also equal to the rank of its row vector group"? How to understand the relationship between the rank of matrix and the rank of vector group, please click in detail
- 7. Let a be mxn real matrix and prove rank (ATA) = rank (a) emergency
- 8. It is proved that the mxn matrix A with rank r (r > 0) can be decomposed into the sum of R mxn matrices with rank 1 Is m x n matrix Detailed process
- 9. Let a be an sxn matrix and B be an mxn matrix composed of the first m rows of A. It is proved that if the rank of the row vector group of a is r, then R (b) > = R + m-s
- 10. Which of the following objects does hastow describe? A. Equivalence relation B. Partial order relation C. Digraph D. Undirected graph
- 11. 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
- 12. Properties of matrix rank 4 If P and Q are reversible, then R (PAQ) = R (a)
- 13. 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)
- 14. 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
- 15. Why is invertible matrix full rank?
- 16. 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
- 17. 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?
- 18. Let λ = 2 be an eigenvalue of invertible matrix A, then matrix (13a) - 1 must have an eigenvalue equal to______ .
- 19. 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;
- 20. Let 2 be an eigenvalue of invertible matrix A, then an eigenvalue of 3A ^ 2 + e is