query: Algebraic proof of equality of characteristic polynomials for AB and BA
positive_passages.docid: 31606
positive_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 132213
negative_passages.text: Is every real monic polynomial the characteristic polynomial of a real matrix?
negative_passages.docid: 62237
negative_passages.text: Characteristic polynomial equals minimal polynomial iff $x, Mx, \ldots, M^{n-1} x$ are linearly independent
negative_passages.docid: 133573
negative_passages.text: characteristic polynomial of the adjacency matrix of a tree
negative_passages.docid: 66709
negative_passages.text: Are the matrix products $AB$ and $BA$ similar?
negative_passages.docid: 53113
negative_passages.text: $I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
negative_passages.docid: 96919
negative_passages.text: Characteristic equation of a recurrence relation
negative_passages.docid: 18282
negative_passages.text: Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
negative_passages.docid: 149364
negative_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 85039
negative_passages.text: Purely "algebraic" proof of Young's Inequality
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 101313
negative_passages.text: Minimal polynomial, determinants and invertibility
negative_passages.docid: 89553
negative_passages.text: proof that every finite matrix has an annihilating polynomial
negative_passages.docid: 88349
negative_passages.text: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
negative_passages.docid: 134709
negative_passages.text: Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions
negative_passages.docid: 17391
negative_passages.text: Diagonalisation and characteristic polynomial