query: Is all of eigenvalues of $A^n$ in a form $\lambda^n$, where $\lambda$ is an eigenvalue of $A$?
positive_passages.docid: 153432
positive_passages.text: Question on the proof of the spectral mapping theorem for polynomials
negative_passages.docid: 45527
negative_passages.text: Do real matrices always have real eigenvalues?
negative_passages.docid: 158205
negative_passages.text: If $A+A^T$ is negative definite, then the eigenvalues of $A$ have negative real parts?
negative_passages.docid: 72046
negative_passages.text: Prove all eigenvalues of $A^*A$ are non-negative
negative_passages.docid: 19649
negative_passages.text: A question about the proof of "a symmetric matrix has real eigenvalues".
negative_passages.docid: 115467
negative_passages.text: Eigenvalues of Householder matrix
negative_passages.docid: 120933
negative_passages.text: A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity
negative_passages.docid: 135420
negative_passages.text: Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
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: 35013
negative_passages.text: Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
negative_passages.docid: 118283
negative_passages.text: Show that if $A^{n}=I$ then $A$ is diagonalizable.
negative_passages.docid: 11358
negative_passages.text: Eigenvalues of the Lagrangian?
negative_passages.docid: 73952
negative_passages.text: Upper bound for the sum of absolute values of the eigenvalues
negative_passages.docid: 16439
negative_passages.text: What are the eigenvalues of matrix that have all elements equal 1?
negative_passages.docid: 111366
negative_passages.text: Does there exist a symmetric matrix $A$ such that $2^{\sqrt{n}}\le |\operatorname{Tr}(A^n)|\le2020 \ \cdot 2^{\sqrt{n}}$ for all $n$
negative_passages.docid: 144898
negative_passages.text: Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
negative_passages.docid: 50384
negative_passages.text: A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum