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Results tagged with eigenvalues
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user 160416
eigenvalues of matrices or operators
4
votes
Accepted
Similarity of two matrices
I will show that it is not possible for $\phi=\pi/2$, so it is certainly not for general $\phi$. (actually, I don't think that it is possible for any single $\phi$ except $0$ and $\pi$, by an analogou …
- 3,446
5
votes
Accepted
Eigenvalues invariant under 90° rotation
$$PXP^{-1}=Y$$
$$PYP^{-1}=X$$
$$QXQ^{-1}=X$$
$$QYQ^{-1}=-Y$$
from which it follows that
$$P(X+iY)P^{-1}=Y+iX=i(X-iY)$$
$$Q(X+iY)Q^{-1}=X-iY$$
This shows that $X+iY$ is conjugate to $i(X+iY)$, so its eigenvalues …
- 3,446
6
votes
On a matrix problem in the field $\mathbb F_2$
Some computation in sage yielded the following example, with $n=8$ and $P$ the cyclic permutation $(12345678)$:
$$M=\left(
\begin{array}{cc}
0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\
0 & 0 & 1 & 1 & 1 & …
- 3,446
20
votes
Accepted
Eigenvalue pattern
Thus the eigenvalues of $A$ are those of $\prod N_{\mu_i}$ plus those of $\overline{\prod N_{\mu_i}}$, which are their complex conjugates. … Moreover, since $N_\mu$ has determinant $1$, so does $\prod N_{\mu_i}$, so its two eigenvalues are inverses of each other. …
- 3,446