query: Trace of a matrix, characteristic polynomial
positive_passages.docid: 1973
positive_passages.text: Traces of all positive powers of a matrix are zero implies it is nilpotent
negative_passages.docid: 129743
negative_passages.text: $A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
negative_passages.docid: 104293
negative_passages.text: How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
negative_passages.docid: 52528
negative_passages.text: Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
negative_passages.docid: 150387
negative_passages.text: Questions about matrix rank, trace, and invertibility
negative_passages.docid: 13020
negative_passages.text: Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$?
negative_passages.docid: 15197
negative_passages.text: Relation between trace and rank for projection matrices
negative_passages.docid: 109471
negative_passages.text: The eigenvectors of the transpose operator
negative_passages.docid: 44371
negative_passages.text: Finding trace and determinant of linear operator
negative_passages.docid: 29583
negative_passages.text: Characterization of the trace function
negative_passages.docid: 127620
negative_passages.text: Matrix exponential of a traceless $2\times2$ complex matrix
negative_passages.docid: 31606
negative_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 35247
negative_passages.text: The characteristic and minimal polynomial of a companion matrix
negative_passages.docid: 116820
negative_passages.text: If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
negative_passages.docid: 133573
negative_passages.text: characteristic polynomial of the adjacency matrix of a tree
negative_passages.docid: 155537
negative_passages.text: Intuition of the cyclic trace property of matrix products and relation to the determinant?
negative_passages.docid: 23224
negative_passages.text: $\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$