Let ${A}$ be a $2 \times 2$ matrix. For every two-dimensional vector ${v}$, there...
4517
Showing a $2\times2$ matrix is invertible
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
55787
Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$?
4151
Every subspace of a vector space has a complement
144898
Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
81879
$Av=λv$ basis proof problems
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
144082
Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
131972
All nilpotent $2 \times 2$ matrices satisfy $A^{2}=0$
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
89089
Prove that there is a unique inner product on $V$
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
22410
Find a symmetric matrix $B$ such that for every $3\times 1$ matrix $\text{x}$
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$