Number of Jordan boxes of size j for eigenvalue $\lambda$ is $2\dim\ker(A-\lambda I)^j-\dim\ker(A-\lambda I)^{j+1}-\dim \ker(A-\lambda I)^{j-1}$
97574
Jordan form, number of blocks.
9220
If $\lambda$ is an eigenvalue of $A^2$, then either $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A$
59973
Eigenvalues and power of a matrix
19132
Similar matrices have the same eigenvalues with the same geometric multiplicity
66842
Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid
4509
Proof that an involutory matrix has eigenvalues 1,-1
135316
A basic question on diagonalizability of a matrix
55230
Dimension of set of commutable matrices
149086
Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
73952
Upper bound for the sum of absolute values of the eigenvalues
6746
What is the Relationship between the Rank and the Number of Eigenvalues?
99685
Matrix exponential for Jordan canonical form
90576
Symmetric matrix eigenvalues
124583
A question about eigenvalues of $5\times5$ matrix
49158
Multiplicity of eigenvalues