New posts in Eigenvalues Eigenvectors

Finding eigenvalues of linear transformation given by matrix conjugation

If $A$ is a matrix such that $A^T = A^2$, what are eigenvalues of $A$?

$AD$ has exactly one negative eigenvalue if $v^T A v > 0$ and $D = \mbox{diag}(-1,1,1)$

Is $\left(\begin{smallmatrix}0&0&1\\1&0&0\\ 0&1&0\end{smallmatrix}\right)$ diagonalizable over $\mathbb{Z}_2$?

How can I find real, symmetric matrices $A,B$ such that $Ax =\lambda B x $ has no real eigenvalues and eigenvectors?

Is there a way to determine the eigenvectors of a matrix without working out the eigenvalues?

If for invertible matrices $A$ and $X$, $XAX^{-1}=A^2$ then eigenvalues of $A$ are $n^{th}$ roots of unity.

$T:\Bbb{R}^2\rightarrow\Bbb{R}^2$ has 2 distinct eigenvalues. Showing that $v$ or $T(v)− \lambda_1v$ are eigenvectors of $T$

Is the rank of a matrix equal to the number of non-zero eigenvalues?

Can an Perron eigenvector of a non-symmetric irreducible nonnegative matrix be also a Perron eigenvector of its transpose?