User learner - Mathematics Stack Exchange

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4

12

votes

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118

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Let $A$ and $B$ be $n \times n$ real matrices such that $AB=BA=0$ and $A+B$ is invertible

linear-algebra matrices

mar 26 at 3:45 julien 22.7k

5

8

votes

4

answers

178

views

The minimum value of $a^2+b^2+c^2+\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}?$

inequality

mar 29 at 8:36 Inceptio 4,665

2

7

votes

3

answers

95

views

Find the limit of $ x_n = \prod_{j=2}^{n} \left(1 - \frac{2}{j(j+1)}\right)^2$

sequences-and-series limit

may 3 at 11:32 robjohn♦ 59.6k

4

7

votes

9

answers

777

views

If $x \neq 0,y \neq 0,$ then $x^2+xy+y^2$ is …

algebra-precalculus

apr 4 at 13:00 Seirios 8,917

2

7

votes

3

answers

80

views

$\lim_{n \to \infty} n \int_0^1 x^np(x) \, dx=$? , where $p(x)$ is a polynomial

integral

feb 22 at 17:04 Seirios 8,917

4

6

votes

2

answers

118

views

$5 \frac {3}{} \times 3 \frac {}{2}=19$?

arithmetic

mar 30 at 12:00 Michael Hardy 48.1k

2

6

votes

1

answer

210

views

Let $f$ be a non-constant entire function such that $\left \lvert f(z) \right\lvert=1$ for every $z$ with $\left \lvert z \right\lvert=1$.

complex-analysis

dec 8 at 6:25 Cameron Buie 27.6k

5

votes

4

answers

74

views

For $n >1$,let $\displaystyle f(n)$ be the number of $n \times n$ real matrices $A$ such that $A^2+I=0.$

linear-algebra matrices

may 19 at 3:55 learner 1,935

2

5

votes

3

answers

71

views

How to prove $\lim_{n \to \infty} \cos \dfrac {\pi}{2^2}\cos \dfrac {\pi}{2^3}\cos \dfrac {\pi}{2^4}…\cos \dfrac {\pi}{2^n}=\dfrac {2}{\pi}$

real-analysis limit

apr 3 at 4:59 André Nicolas 161k

2

5

votes

5

answers

125

views

What is the number of distinct homomorphism from $\Bbb Z/5 \Bbb Z$ to $\Bbb Z/7 \Bbb Z$

abstract-algebra group-theory finite-groups abelian-groups cyclic-groups

mar 31 at 18:18 learner 1,935

5

votes

2

answers

75

views

How many complex numbers $z=x+iy$ are there such that $x+y=1$ and $e^{i(x^2+y^2)}=1.$

complex-analysis

feb 21 at 17:53 learner 1,935

4

votes

2

answers

41

views

Check whether the following polynomial is irreducible over $\mathbf Q$

abstract-algebra polynomials

15h ago Git Gud 5,821

4

votes

4

answers

62

views

Find the value of $\int \frac {du}{(a-u^2)^2}$

integration

apr 16 at 18:41 Sagarika 361

3

4

votes

2

answers

219

views

Let $\displaystyle f$ be an analytic function defined on $\Bbb D=\{z \in \Bbb C:|z|<1\}$

complex-analysis

mar 30 at 14:51 Ayman Hourieh 11.2k

1

4

votes

3

answers

200

views

The value of $(2^n+3^n+4^n)^{1/n}$ as $n \rightarrow \infty?$

analysis limit

feb 19 at 14:30 P.. 8,905

4

votes

3

answers

112

views

Finding the number of eigenvector(s) of non-zero linear transformation $T$ to $R$

linear-algebra

feb 12 at 17:24 Taxi Driver 7,262

4

votes

2

answers

102

views

Let $f:\mathbb R \rightarrow \mathbb R$ be a differentiable even function

real-analysis analysis

jan 17 at 6:59 Antonio Vargas 6,700

4

votes

2

answers

144

views

The minimum value of $|z+1|+|z-1|+|z-i|$ for $z \in \mathbb C?$

complex-analysis

jan 9 at 17:26 JohnD 3,490

4

votes

3

answers

214

views

The set of limit points of the sequence $1,\frac12,\frac14,\frac34,\frac18,\frac38,\frac58,\frac78,\frac1{16},\frac3{16},\ldots$

real-analysis sequences-and-series

dec 31 at 23:59 Community♦ 1

4

votes

3

answers

106

views

$A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?

linear-algebra matrices

dec 31 at 15:42 Sugata Adhya 1,606

1

3

votes

3

answers

48

views

Problem related to a series

sequences-and-series

may 10 at 18:26 robjohn♦ 59.6k

1

3

votes

2

answers

50

views

If $E$ is infinite and countable…

elementary-set-theory

apr 16 at 23:45 Asaf Karagila 91k

3

votes

2

answers

52

views

If $f$ is differentiable on $[0,1]$,then $f(1)-f(0)=\dfrac {f'(x)}{2x}$ has at least one solution in $(0,1)$.

real-analysis

apr 5 at 11:53 Did 103k

2

3

votes

2

answers

104

views

Multiple Choice question about an $n \times n$ matrix $A$ with real or complex entries, and such that $A^3=0$

linear-algebra matrices

mar 29 at 5:21 Andres Caicedo 24.4k

3

votes

3

answers

36

views

Find a $2$ by $3$ system $Ax=b$ whose general solution is…

linear-algebra

mar 28 at 16:03 Abhra Abir Kundu 3,437

1

3

votes

1

answer

67

views

Problems related with a linear transformation

linear-algebra

mar 27 at 6:17 learner 1,935

3

votes

2

answers

78

views

Let $a,b,c$ are positive real numbers such that $b^2+c^2<a<1.$

linear-algebra

mar 20 at 14:43 Rustyn Yazdanpour 2,145

3

votes

1

answer

67

views

$\int \frac{\sqrt x}{1+\sqrt[4]{x-b}}dx=?$

integration

feb 28 at 15:21 Steve Kass 743

3

votes

4

answers

90

views

Find the value of the following expression

algebra-precalculus

feb 20 at 18:38 Clayton 7,866

1

3

votes

4

answers

159

views

Let $f: ~\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{-1}^{x}f(t)dt=0$ for all $x \in [-1,1]$

real-analysis analysis

dec 21 at 11:42 Nameless 7,937

learner

108 Questions