If for linear operator $A:E\to E$, $A^k=0$, then $A^n=0$
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
34714
What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
116558
Consider two linear operators $\hat{A}$ and $\hat{B}$. Show that $e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2}$
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
32103
Show that for a $2\times 2$ matrix $A^2=0$
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
44596
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
58741
Operator Exponential $e^A e^B = e^{A+B}$
94077
Proof of linear independence of $e^{at}$
67645
Prove that $\displaystyle{\lim_{n \to \infty}a_n ^{1/k}}= a^{1/k}$ if $a_n \ge 0$ for all $n$ and $\displaystyle{\lim_{n \to \infty}a_n}= a$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$