query: $A$ is hermitian $\Leftrightarrow$ $A$ has real eigenvalues?
positive_passages.docid: 150376
positive_passages.text: Does Real Eigenvalues mean it is an hermitian Matrix
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 116539
negative_passages.text: Eigenvalues of matrix satisfying $A^2 = A$
negative_passages.docid: 27778
negative_passages.text: Eigenvalues of a real skew symmetric matrix
negative_passages.docid: 59397
negative_passages.text: Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 45527
negative_passages.text: Do real matrices always have real eigenvalues?
negative_passages.docid: 98135
negative_passages.text: Show that the determinant of $A$ is equal to the product of its eigenvalues
negative_passages.docid: 135420
negative_passages.text: Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
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: 72046
negative_passages.text: Prove all eigenvalues of $A^*A$ are non-negative
negative_passages.docid: 158406
negative_passages.text: $A,B$ be Hermitian.Is this true that $tr[(AB)^2]\le tr(A^2B^2)$?
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: 119387
negative_passages.text: If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
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: 9220
negative_passages.text: If $\lambda$ is an eigenvalue of $A^2$, then either $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A$
negative_passages.docid: 115296
negative_passages.text: Under what conditions does a matrix $A$ have a square root?