New posts in nilpotence

Prove that all nxn nilpotent matrices of order n are similar.

linear-algebra matrices nilpotence

degree of nilpotent matrix

linear-algebra matrices nilpotence

Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.

matrices nilpotence

If $N^n=0$ but $N^{n-1}\neq 0$, then there is no $n\times n$ matrix $A$ such that $A^2=N$

linear-algebra matrices nilpotence characteristic-polynomial

Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$

linear-algebra matrices nilpotence

Dual number $(a+b\varepsilon)$ raised to a dual power, e.g. $(a+b\varepsilon)^{(c+d\varepsilon)}$

derivatives nilpotence hypercomplex-numbers

If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent

linear-algebra linear-transformations nilpotence

How to apply Vandemonde determinant to show nilpotent here?

linear-algebra matrices nilpotence

$T \in \text{Hom}V $ is nilpotent implies $I - T$ invertible [duplicate]

vector-spaces proof-writing linear-transformations problem-solving nilpotence

Lifting idempotents modulo a nilpotent ideal

abstract-algebra ring-theory noncommutative-algebra nilpotence

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

linear-algebra matrices examples-counterexamples nilpotence

Generalize exterior algebra: vectors are nilcube instead of nilsquare

abstract-algebra vector-spaces tensor-products quotient-spaces nilpotence

Why are eigenvalues of nilpotent matrices equal to zero? [duplicate]

linear-algebra matrices nilpotence

$A$ is normal and nilpotent, show $A=0$

linear-algebra matrices nilpotence

All nilpotent $2\times 2$ matrices

linear-algebra abstract-algebra matrices jordan-normal-form nilpotence

Nilpotent matrix and relation between its powers and dimension of kernels

linear-algebra matrices nilpotence

$a+1,a-1$ invertible for nilpotent element

abstract-algebra ring-theory nilpotence

Direct proof that nilpotent matrix has zero trace

linear-algebra matrices trace nilpotence

$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent [duplicate]

abstract-algebra ring-theory nilpotence

Construct a $2022\times 2022$ matrix $A$ such that $A^{2022}=0$ but $A^{2021} \neq 0$

linear-algebra matrices nilpotence