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Coriolanus
  • Member for 7 years, 2 months
  • Last seen this week
11 votes

Show that the eigenvalues of $AA^T$ and $A^TA$ are non-negative.

4 votes
Accepted

Can two uncountable disjoint sets be dense in $[0,1]$?

4 votes

Translation- and linear transformation- invariance of Lebesgue measure, Rudin

4 votes

Two ways of saying span

3 votes
Accepted

$P \in \text {SO}_{n} (\Bbb R)$ if $P$ is orthogonal and $P^{-1} A P$ is diagonal with $A$ symmetric?

3 votes

Let $A \in \mathbb{R}^{n \times n}$ such that for all $x \in \mathbb{R}^n, x^TAx \geq 0$. Prove that $\ker(A) = \ker(A^T)$

3 votes
Accepted

Prove an idempotent invertible 2x2 matrix in general linear group $\text{GL}_2(\mathbb{R})$ must be the identity

3 votes
Accepted

Linear algebra skew symmetric

3 votes
Accepted

Kernel and image of a product of two rectangular matrices

3 votes
Accepted

If $S$ is symmetric positive definite and $SA$ symmetric, is then $A$ symmetric?

3 votes
Accepted

$u,v$ two endomorphisms such as $u\circ v = v \circ u $ and $\ker (u) \cap \ker (v) = \{0\}$, Show that $GL(E) \cap Span(u,v) \ne \emptyset$

3 votes

Eigenvector of A by $A^2$

3 votes
Accepted

Define subspaces $U_1 \leq V$ and $U_2 \leq V$, can I then claim $\dim(U_1+U_2)=\dim V$?

2 votes
Accepted

Proving there is no matrix in $\mathbb{F}_2^{2\times2}$ that commutes with every invertible matrix

2 votes
Accepted

Find a $\bar v$ with $\|\bar v\|_\infty=\alpha$ such that $\langle u \, , \bar v \rangle = - \|u\|_1\|v\|_\infty = -\alpha\|u\|_1$

2 votes
Accepted

How to prove $\det(tI-BA^T)=\det(tI-B^TA)t^{m-n}$?

2 votes
Accepted

Rudin, Riesz Representation Step X: Why do we need $|a|$?

2 votes

If a linear map $H:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}$ is injective...

2 votes

If $~A~$ is a $~n\times n~$ matrix in $~\mathbb R~$, $~A^3=I~$ and $~AB=-BA~$, how to prove $~\text{tr}(B)=0~$?

2 votes
Accepted

Eigenvalues of a matrix which has to satisfy an equation

2 votes
Accepted

Determine the rank of $AB$, given matrices $A$ which is $m \times n$ and $B$ which is $n \times $p$ - proof assistence

2 votes
Accepted

Showing that $A^2=I$ implies $A$ is diagonalizable

2 votes
Accepted

Generating set for $SL_2(\mathbb{C})$

1 vote
Accepted

Prove that there is a base in $R^n$ that matches criteria

1 vote
Accepted

When do the zero rows of the reduced system determine the column space?

1 vote
Accepted

Let $U \in \mathbb{R}^{m \times n}$, $V \in \mathbb{R}^{k \times n}$,

1 vote
Accepted

$23$ odd subsets of $\{1,2,...26\}$ such that intersection of every two is even. Can we find another odd set...

1 vote
Accepted

Cancellation properties of matrix multiplication

1 vote

How to find the eigenvalues of this matrix in a simple way?

1 vote
Accepted

Perpendicular Vectors on Unit Sphere induce bound on components