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algo
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4 votes
2 answers
66 views

Prove that $v\in V$ such that $\| v\|=1$ and $\| T(v)\|_W = \max\limits_{\Vert u \Vert_V = 1} \Vert T(u) \Vert_W$ is an eigenvector of $T^*T$

3 votes
1 answer
48 views

Find the solutions of : $(x^2-2)x^2y''-(x^2+2)xy'+(x^2+2)y=0$

3 votes
1 answer
93 views

$A,B$ matrices $n \times n$ have the same eigenvectors. $M_A=(x+1)^2, P_B=x^5.$ Prove $B^3=0.$

3 votes
1 answer
57 views

Equivalence-relations overcounting

3 votes
2 answers
57 views

$AB=Y = y + y'(x) (X-x)$ $PG= Y = y - \frac{1}{y'(x)} (X-x)$ Find the curves such that $PM=MG$.

3 votes
4 answers
142 views

Prove $f$ injective implies $o(f(g)) = o(g)$.

3 votes
1 answer
84 views

Prove $\{\sigma\in S_\Bbb N\mid\sigma(x)= x\text{ for all but finitely many }x\in\Bbb{N}\}$ is not finitely generated

3 votes
1 answer
51 views

Let $\mathbb{Z}^n, n\in\mathbb{N}$ be a free abelian group. Prove the intersection of index $h$ subgroups is the subgroup $(h\mathbb{Z})^n$.

3 votes
4 answers
148 views

Let $G$ be a group, $|G|=12$, $H\leq G, |H|=6 , \exists x\in G ,x\notin H $ such that $o(x)=2$. Prove $|Z(G)|=12$ or $|Z(G)|=2$.

2 votes
1 answer
64 views

Let $G$ be a group, $|G|=n$. Suppose $\forall d\in \mathbb{N}$ such that $d\mid n$, there are at most $d$ elements s.t. $x^d=1$. Prove $G$ is cyclic.

2 votes
2 answers
65 views

Let $G$ be a group with $n$ conjugacy classes. Prove there is a maximum $2^{n-1}$ normal subgroups.

2 votes
2 answers
62 views

Finitely generated abelian groups clarification

2 votes
1 answer
33 views

Prove $\phi^{-1}(\phi(H))=\langle H,\ker\phi \rangle$

2 votes
1 answer
60 views

Distance between matrix and vector subspace

2 votes
0 answers
45 views

Wronskian and extremum

2 votes
0 answers
28 views

Let $X$ be uniformly distributed on $[0, 1]$. Let $Y = X^{\frac{1}{\beta}} . \beta\neq0$ Find the density function for $Y$.

2 votes
1 answer
63 views

$x^2y''+(3x^2+4x)y'+2(x^2+3x+1)y=0$

2 votes
1 answer
81 views

For each $w \in F$, show $\sqrt{w}:= \left\{ a\in F | a^n=w\text{ for some }n\in \mathbb N \right\}$ is finite

2 votes
1 answer
47 views

Which cardinality has the given set?

2 votes
0 answers
93 views

How many groups are there of order $11^2\times 13^2$ up to isomorphism?

2 votes
0 answers
74 views

Why $|P(\mathbb N)|>|\mathbb N|$

2 votes
0 answers
71 views

$f$ surjective iff for every $g:B \rightarrow C, h:B \rightarrow C$ exist $g \circ f=h \circ f \implies g=h.$

2 votes
2 answers
96 views

cardinality of some subsets of the power sets of $\mathbb Z$ and $\mathbb R$

2 votes
2 answers
186 views

Integrating factor of $x^2ydx-(x^3+y^3)dy=0$

2 votes
1 answer
41 views

Solve : $y''+a^2y=\sin(bx) ,a,b\in \mathbb{R}$

2 votes
1 answer
72 views

Find $T^*\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ in an inner product space

2 votes
2 answers
60 views

Find power series solution for $y''-xy=0$ close to $x=0$.

2 votes
0 answers
30 views

$A_1, A_2 \in M_2(\mathbb{R})$, symmetric and nonsingular matrix. Prove $A_1,A_2$ are not congruent $\implies A_1,A_2$ simultaneously diagonalizable.

2 votes
0 answers
51 views

$y''+(5+2\cos x)y=0, y(0)=0, y'(0)=1$. Find the upper bound and lower bound of the times that $y(x)=0$ in $[0,100]$ such that $y(x)$ is the solution. [closed]

2 votes
0 answers
41 views

$V$ is a vector space over $\mathbb{F}, dimV<\infty$. $T:V \to V $ .Prove that exist T-invariant subspace $W$ of $V$ such that $P_{T|W}=m_{T|W}=m_T$.

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