query: Show that the eigenvalues of the cycle $C_n$ are $λ_j=2 \cos(\frac{2πj}{n})$
positive_passages.docid: 142202
positive_passages.text: eigenvalues of cycle graph and its complement graph
negative_passages.docid: 119808
negative_passages.text: Proving that $n$-cycle has order $n$
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: 72046
negative_passages.text: Prove all eigenvalues of $A^*A$ are non-negative
negative_passages.docid: 28584
negative_passages.text: Eigenvalues and eigenspaces of AB
negative_passages.docid: 4517
negative_passages.text: Showing a $2\times2$ matrix is invertible
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: 8192
negative_passages.text: Simple proof of showing the Harmonic number $H_n = \Theta (\log n)$
negative_passages.docid: 98135
negative_passages.text: Show that the determinant of $A$ is equal to the product of its eigenvalues
negative_passages.docid: 45626
negative_passages.text: How do I calculate the eigenvalues of the positive partial transpose of this two-qubit state?
negative_passages.docid: 75461
negative_passages.text: If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
negative_passages.docid: 149609
negative_passages.text: Conditions on cycle types for permutations to generate $S_n$
negative_passages.docid: 88349
negative_passages.text: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
negative_passages.docid: 106024
negative_passages.text: The eigenvalues and corresponding eigenvectors for the matrix
negative_passages.docid: 149294
negative_passages.text: How do i prove how $S_5$ is generated by a two cycle and a five cycle?
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 150228
negative_passages.text: If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.