query: Eigenvalue of a Polynomial
positive_passages.docid: 104293
positive_passages.text: How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
negative_passages.docid: 125802
negative_passages.text: Why is EigenValues returning Root expressions?
negative_passages.docid: 76477
negative_passages.text: Eigenvalues with transpose question.
negative_passages.docid: 149629
negative_passages.text: The Eigenvalues of a block matrix
negative_passages.docid: 86940
negative_passages.text: Proving an inequality in Eigenvalues of a matrix
negative_passages.docid: 124583
negative_passages.text: A question about eigenvalues of $5\times5$ matrix
negative_passages.docid: 149916
negative_passages.text: Minimum eigenvalue and singular value of a square matrix
negative_passages.docid: 59973
negative_passages.text: Eigenvalues and power of a matrix
negative_passages.docid: 149923
negative_passages.text: eigenvalues of A - aI in terms of eigenvalues of A
negative_passages.docid: 4952
negative_passages.text: Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
negative_passages.docid: 49158
negative_passages.text: Multiplicity of eigenvalues
negative_passages.docid: 10001
negative_passages.text: Prove that the only eigenvalue of a nilpotent operator is 0?
negative_passages.docid: 77388
negative_passages.text: Differentiation operator and eigenvalues
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 55119
negative_passages.text: Proof that the coefficients of a polynomial are real
negative_passages.docid: 41932
negative_passages.text: Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
negative_passages.docid: 35080
negative_passages.text: If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$