query: Proving that matrix is similar to its transpose
positive_passages.docid: 42761
positive_passages.text: Matrix is conjugate to its own transpose
negative_passages.docid: 6091
negative_passages.text: Similarity of products $AB$ and $BA$ of square matrices
negative_passages.docid: 10083
negative_passages.text: Determinant of matrix times a constant.
negative_passages.docid: 139685
negative_passages.text: If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 61538
negative_passages.text: Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
negative_passages.docid: 88712
negative_passages.text: Determining a matrix from its characteristic polynomial
negative_passages.docid: 55272
negative_passages.text: Prove that all nxn nilpotent matrices of order n are similar.
negative_passages.docid: 146715
negative_passages.text: A square matrix has the same minimal polynomial over its base field as it has over an extension field
negative_passages.docid: 15202
negative_passages.text: the root of $N$th transpose matrix
negative_passages.docid: 77587
negative_passages.text: Cross product: matrix transformation identity
negative_passages.docid: 30665
negative_passages.text: Elegant proofs that similar matrices have the same characteristic polynomial?
negative_passages.docid: 7712
negative_passages.text: How to prove the both identity (matrix)
negative_passages.docid: 136389
negative_passages.text: Finding an isomorphic subring of matrices
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 48658
negative_passages.text: Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
negative_passages.docid: 33355
negative_passages.text: Proving that matrix in equation is invertible