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Results tagged with eigenvalues
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user 38468
eigenvalues of matrices or operators
3
votes
Accepted
Proving 2 matrices have the same trace
Let's call $C=A-B$. Then you have $C^2=I_n$ and $BC-CB$ is invertible. You want to show that $C$ has an equal dimension of $1$ and $(-1)$ eigenspaces, which in turn implies both the equality $tr(A)=tr …
- 5,186
10
votes
Accepted
Eigenvalues of a matrix with entries involving combinatorics
Clearly, these statements 1 and 2 together imply that the eigenvalues
are $1,l,\ldots, l^{n-1}$.
We will assume throughout that $l\geq 2$, otherwise the statement is obvious. …
- 5,186
2
votes
When is this matrix singular?
For $\phi_j=0$ and $t_k=k$ you have (up to a constant) the matrix $A_{jk}= \lambda_j^k - \lambda_j^{-k}$ where $\lambda_j=\exp( i w_j)$. You can factor out $\lambda_j-\lambda_j^{-1}$
to get a matrix $ …
- 2,251