If $A_{n\times n}$ is nilpotent matrix then $\beta = (y, Ay,A^2y, \ldots, A^{k-1}y)$ is the basis of vector space $\mathbb R^n$.
115273
Nilpotent matrix and basis for $F^n$
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
130498
Linear algebra proof regarding matrices
154724
Every vector space has a basis
78263
Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
113474
An $n \times n$ matrix $M$ of integers has the property that $M_{ab} = M_{xy}$ iff $a+b=x+y$. How many distinct elements are there in $M$?
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
87692
Basis and dimension of vector space
144082
Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
54479
If $x,y$ are nilpotent and commute, $x+y $ is nilpotent.
55062
$2\times 2$ matrix $C=AB-BA$
94929
Proof that the all bases of a subspace V consist of the same number of vectors?