Question

If $p$ and $q$ are orthogonal projections in $\mathbb{R}^n$, then $\Vert p(x)- q(x)\Vert\leq \Vert x\Vert$

score 444 · Answer 1 · 2026-03-27 07:17:03

444

Views

If $p$ and $q$ are orthogonal projections in $\mathbb{R}^n$, then $\Vert p(x)- q(x)\Vert\leq \Vert x\Vert$

Published on 27 Mar 2026 - 7:17

score 294 · Answer 2 · 2020-04-09 01:38:34

294

Views

Various methods used to evaluate $\int_0^1 \frac{\sin(\ln x)}{\ln x}\,dx$

Published on 09 Apr 2020 - 1:38

score 252 · Answer 3 · 2020-04-09 12:18:48

252

Views

Compact embedding of $W^{1,1}_0(\Omega)$ into $L^1(\Omega)$ one dimension without mollification

Published on 09 Apr 2020 - 12:18

score 2.8k · Answer 4 · 2020-04-10 01:03:17

2.8k

Views

A commutative ring R is an integral domain $\iff a,b,c \in R, a \neq0, ab=ac \implies b=c$.

Published on 10 Apr 2020 - 1:03

score 1.2k · Answer 5 · 2026-03-27 18:26:15

1.2k

Views

Symmetric rational function is a rational function in the elementary symmetric polynomials.

Published on 27 Mar 2026 - 18:26

score 330 · Answer 6 · 2020-04-11 04:31:33

330

Views

For an integral domain $D$, $na = 0$ where $n \in \mathbb{Z}, n\neq 0$ for some $a \in D - \{0\}$, then $D$ is of finite characteristic.

Published on 11 Apr 2020 - 4:31

score 134 · Answer 7 · 2026-02-23 02:50:11

134

Views

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

Published on 23 Feb 2026 - 2:50

score 74 · Answer 8 · 2026-03-27 02:39:35

74

Views

The power of induction.

Published on 27 Mar 2026 - 2:39

score 633 · Answer 9 · 2020-04-12 23:49:21

633

Views

$\phi : R \to R’$ is an onto ring homomorphism. $1 \in R$. Then $\phi(1) \in R’$ is the unit element of $R’$.

Published on 12 Apr 2020 - 23:49

score 96 · Answer 10 · 2020-04-14 02:27:55

96

Views

Show $(29,x^2+1)\subset\mathbb{Z}[x]$ is not a maximal ideal

Published on 14 Apr 2020 - 2:27

score 89 · Answer 11 · 2020-04-14 03:46:27

89

Views

Let $A \in M_n(F[x])$ be an invertible matrix. Prove that $\deg(\det A)=0$.

Published on 14 Apr 2020 - 3:46

score 290 · Answer 12 · 2026-03-30 06:48:44

290

Views

Find all $f$ such that $f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2},$

Published on 30 Mar 2026 - 6:48

score 83 · Answer 13 · 2026-03-30 07:11:45

83

Views

Evaluation of limit involving product of cosines

Published on 30 Mar 2026 - 7:11

score 27 · Answer 14 · 2026-03-30 07:05:49

27

Views

Evaluation of a limit using another

Published on 30 Mar 2026 - 7:05

score 481 · Answer 15 · 2026-03-27 21:34:37

481

Views

Is Shadowing Lemma specific to hyperbolic dynamical systems?

Published on 27 Mar 2026 - 21:34

List Question

If $p$ and $q$ are orthogonal projections in $\mathbb{R}^n$, then $\Vert p(x)- q(x)\Vert\leq \Vert x\Vert$

Various methods used to evaluate $\int_0^1 \frac{\sin(\ln x)}{\ln x}\,dx$

Compact embedding of $W^{1,1}_0(\Omega)$ into $L^1(\Omega)$ one dimension without mollification

A commutative ring R is an integral domain $\iff a,b,c \in R, a \neq0, ab=ac \implies b=c$.

Symmetric rational function is a rational function in the elementary symmetric polynomials.

For an integral domain $D$, $na = 0$ where $n \in \mathbb{Z}, n\neq 0$ for some $a \in D - \{0\}$, then $D$ is of finite characteristic.

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

The power of induction.

$\phi : R \to R’$ is an onto ring homomorphism. $1 \in R$. Then $\phi(1) \in R’$ is the unit element of $R’$.

Show $(29,x^2+1)\subset\mathbb{Z}[x]$ is not a maximal ideal

Let $A \in M_n(F[x])$ be an invertible matrix. Prove that $\deg(\det A)=0$.

Find all $f$ such that $f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2},$

Evaluation of limit involving product of cosines

Evaluation of a limit using another

Is Shadowing Lemma specific to hyperbolic dynamical systems?

Trending Questions

Popular # Hahtags

Popular Questions