Give a example of 2$\times$2 matrix A such that A has one independent eigenvector while $A^2$ has two independent eigenvectors.
100656
$2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
10828
If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
104293
How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
28584
Eigenvalues and eigenspaces of AB
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
69542
Why do the $n \times n$ non-singular matrices form an "open" set?
116539
Eigenvalues of matrix satisfying $A^2 = A$
4517
Showing a $2\times2$ matrix is invertible
120867
How prove this two symmetric matrices $AB=0$
33591
Product of two matrices sharing the same eigenvector
126064
What are examples of two non-similar invertible matrices with same minimal and characteristic polynomial and same dimension of each eigenspace?
99600
Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
132913
Sum of two eigenvectors for different eigenvalues