Prove rank(λI−A)=rank((λI−A)^2). Given that A is a diagonalizable matrix and λ an eigenvalue of A.
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
64747
If $A^m=I$ then A is Diagonalizable
141628
How did the equation $|A- \lambda I| = 0$ came for finding Eigen values of a Matrix
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
6514
Prove $T$ has at most two distinct eigenvalues
130799
Matrix of rank 1; show that $A^2=cA$ for some scalar $c$.
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
72046
Prove all eigenvalues of $A^*A$ are non-negative
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
35155
To prove Cayley-Hamilton theorem, why can't we substitute $A$ for $\lambda$ in $p(\lambda) = \det(\lambda I - A)$?
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
69606
How to prove rank(A+) is no more than rank(A)?
144898
Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?