query: Is there any way to know the algebraic multiplicity of the $0$ eigenvalue in the minimal polynomial when the rank is $1$?
positive_passages.docid: 14111
positive_passages.text: Determining possible minimal polynomials for a rank one linear operator
negative_passages.docid: 104424
negative_passages.text: If each eigenvalueof $A$ is either $+1$ or $-1$ $ \Rightarrow$ $A$ is similar to ${A^{ - 1}}$
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: 125096
negative_passages.text: Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
negative_passages.docid: 26999
negative_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 89473
negative_passages.text: Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
negative_passages.docid: 88712
negative_passages.text: Determining a matrix from its characteristic polynomial
negative_passages.docid: 117777
negative_passages.text: What are the zero divisors of $C[0,1]$?
negative_passages.docid: 19280
negative_passages.text: Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond
negative_passages.docid: 98656
negative_passages.text: Geometric multiplicity of the largest eigenvalue
negative_passages.docid: 149364
negative_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 71040
negative_passages.text: If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
negative_passages.docid: 153107
negative_passages.text: Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
negative_passages.docid: 103948
negative_passages.text: Minimal polynomial is invariant under field extensions
negative_passages.docid: 48906
negative_passages.text: Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.
negative_passages.docid: 7833
negative_passages.text: Ideal and minimal polynomial
negative_passages.docid: 52621
negative_passages.text: Why is $\det(A - \lambda I)$ zero?