query: Rank of transpose of a matrix.
positive_passages.docid: 28565
positive_passages.text: Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
negative_passages.docid: 111769
negative_passages.text: Why is inverse of orthogonal matrix is its transpose?
negative_passages.docid: 74611
negative_passages.text: $\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
negative_passages.docid: 121157
negative_passages.text: Proof verification: column rank = row rank
negative_passages.docid: 65628
negative_passages.text: what happens to rank of matrices when singular matrix multiply by non-singular matrix??
negative_passages.docid: 67058
negative_passages.text: Prove that $\text{rank}(X^TX)=\text{rank}(X)$
negative_passages.docid: 18939
negative_passages.text: Eigenvalues of the transpose
negative_passages.docid: 10083
negative_passages.text: Determinant of matrix times a constant.
negative_passages.docid: 155451
negative_passages.text: Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
negative_passages.docid: 29788
negative_passages.text: Eigenvalues of a matrix whose square equals its transpose
negative_passages.docid: 64517
negative_passages.text: Prove that row rank of a matrix equals column rank
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 23580
negative_passages.text: Range of A and null space of the transpose of A
negative_passages.docid: 156877
negative_passages.text: Rank-one perturbation proof
negative_passages.docid: 34820
negative_passages.text: Transpose Operator is diagonalizable?
negative_passages.docid: 44383
negative_passages.text: Finding rank of a matrix depending on parameter a
negative_passages.docid: 97487
negative_passages.text: How to prove whether a matrix has rank $1$