User John

15 votes

6 answers

16k views

What is a subsequence in calculus?

asked Sep 23, 2017 at 17:46

8 votes

1 answer

499 views

If $A$ is an $n$ by $n$ integer matrix such that $A^3 = I$, then $\operatorname{tr}(A) = n\mod3$

asked Dec 17, 2018 at 21:22

7 votes

1 answer

576 views

Prove that $tr(A)^p = tr(A^p)\bmod p$ where $A$ is a square integer matrix and $p$ is a prime number.

asked Dec 18, 2018 at 2:29

7 votes

2 answers

14k views

How to solve a system of linear equations modulo n?

asked Dec 7, 2017 at 20:43

6 votes

1 answer

215 views

Let $G$ be a finite matrix group in $GL_2(Q)$ such that every matrix $A\in G$ has integer entries. Prove $A^{12}= I$ for each $A$.

asked Oct 13, 2018 at 10:10

5 votes

3 answers

153 views

Finding the eigenvalues of a linear transformation which takes inputs from the set of all $n\times n$ matrices.

asked Oct 4, 2018 at 3:31

5 votes

4 answers

2k views

Usage of mean value theorem ; bounded derivative and open interval

asked Jan 6, 2018 at 22:21

4 votes

3 answers

260 views

First-order set theory : What is the class of all sets in ZFC?

asked Oct 3, 2017 at 4:42

4 votes

0 answers

649 views

Prove that if every linear operator which commutes with $T$ is a polynomial in $T$, then $T$ admits a cyclic vector $v$ in $V$ (finite dimensional). [duplicate]

asked Sep 12, 2018 at 18:28

4 votes

6 answers

222 views

Explaining the concept of identities in Math to a grade 8 student

asked May 31 at 2:25

3 votes

0 answers

150 views

Limiting probabilities in $M/M/1$ queuing system with uniform bulk arrival rates

asked Nov 20, 2020 at 15:58

3 votes

0 answers

87 views

Renewal Process with continuous interarrival times of finite expectations: prove $E[S_{N(t)+1}^2]=E[X_1^2](m(t)+1) - 2E[X_1] \int_{0}^{t} m(x) dx$

asked Dec 13, 2020 at 13:43

3 votes

3 answers

795 views

Let $f(z)$ be an entire function with an entire inverse. Prove that as $z$ goes to infinity, $|f(z)|$ goes to infinity.

asked Jul 10, 2019 at 19:29

3 votes

2 answers

103 views

How do I prove that if $A \neq B$, then $\{A\} \neq \{B\}$, where $A$, $B$ are sets?

asked Oct 4, 2017 at 21:17

3 votes

3 answers

144 views

Hint required : Why is the integral $\int_0^x \frac{\sin(t)}{1+t}\mathrm{d}t$ positive?

asked Jan 14, 2018 at 23:23

3 votes

1 answer

2k views

Let $A,B$ be $m \times n$ and $n \times m$ matrices, respectively. Prove that if $m > n$, $AB$ is not invertible

asked Jan 25, 2018 at 3:50

3 votes

1 answer

106 views

Show that if $A,B$ are $2\times2$ matrices, then $(AB-BA)^2$ commutes with all $2\times2$ matrices.

asked Jan 28, 2018 at 16:56

2 votes

4 answers

6k views

What does "Consider R as an vector space over Q" mean?

asked Feb 6, 2018 at 2:56

2 votes

1 answer

806 views

Find all $n$ by $n$ matrices $A$ such that $A^2 = A.$ [duplicate]

asked Feb 6, 2018 at 19:29

2 votes

1 answer

311 views

Let $f_n(x)$ be a sequence of integrable functions such that $\lim_{n\to \infty} \int^a_b |f_n(x)|dx=0$. Prove the following

asked Feb 13, 2018 at 1:35

2 votes

1 answer

33 views

Let $S$ be a linearly dependent set. Then, for each $x$ in $S$, is it true that $x$ is in $\operatorname{span}(S\setminus \{x\})$?

asked Mar 12, 2018 at 23:59

2 votes

3 answers

79 views

$A$ , an $n\times n$ matrix has $k$ distinct eigenvalues, then the matrix $A^m$ for some $m>=0$ has the same eigenvalues raised to $m$

asked Mar 22, 2018 at 13:44

2 votes

3 answers

61 views

Prove that the series with terms $a_n$ diverges. [duplicate]

asked Mar 27, 2018 at 21:24

2 votes

1 answer

432 views

Method for evaluating Darboux integrals by a sequence of partitions?

asked Jan 15, 2018 at 3:21

2 votes

1 answer

199 views

Can one apply LHopitals' rule to differentiable functions defined over the naturals?

asked Jan 19, 2018 at 1:39

2 votes

1 answer

741 views

Prove that the product of all the positive divisors of two numbers is equal implies the numbers themselves are equal.

asked Nov 20, 2017 at 5:32

2 votes

2 answers

189 views

Why does every Laurent Series have a singular point on the outer and inner boundary

asked Jul 10, 2019 at 23:22

2 votes

0 answers

45 views

Two random variables $U$, $V$ such that the conditional distribution of $U$ given $V = v$ is $ve^{-u}$ for $u > ln(v)$. Prove the following:

asked Aug 12, 2019 at 17:09

2 votes

2 answers

3k views

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex [duplicate]

asked Sep 26, 2018 at 3:11

2 votes

0 answers

198 views

Application of the cyclic decomposition theorem to a linear transformation

asked Dec 17, 2018 at 4:47

Stack Exchange Network

101 Questions

What is a subsequence in calculus?

If $A$ is an $n$ by $n$ integer matrix such that $A^3 = I$, then $\operatorname{tr}(A) = n\mod3$

Prove that $tr(A)^p = tr(A^p)\bmod p$ where $A$ is a square integer matrix and $p$ is a prime number.

How to solve a system of linear equations modulo n?

Let $G$ be a finite matrix group in $GL_2(Q)$ such that every matrix $A\in G$ has integer entries. Prove $A^{12}= I$ for each $A$.

Finding the eigenvalues of a linear transformation which takes inputs from the set of all $n\times n$ matrices.

Usage of mean value theorem ; bounded derivative and open interval

First-order set theory : What is the class of all sets in ZFC?

Prove that if every linear operator which commutes with $T$ is a polynomial in $T$, then $T$ admits a cyclic vector $v$ in $V$ (finite dimensional). [duplicate]

Explaining the concept of identities in Math to a grade 8 student

Limiting probabilities in $M/M/1$ queuing system with uniform bulk arrival rates

Renewal Process with continuous interarrival times of finite expectations: prove $E[S_{N(t)+1}^2]=E[X_1^2](m(t)+1) - 2E[X_1] \int_{0}^{t} m(x) dx$

Let $f(z)$ be an entire function with an entire inverse. Prove that as $z$ goes to infinity, $|f(z)|$ goes to infinity.

How do I prove that if $A \neq B$, then $\{A\} \neq \{B\}$, where $A$, $B$ are sets?

Hint required : Why is the integral $\int_0^x \frac{\sin(t)}{1+t}\mathrm{d}t$ positive?

Let $A,B$ be $m \times n$ and $n \times m$ matrices, respectively. Prove that if $m > n$, $AB$ is not invertible

Show that if $A,B$ are $2\times2$ matrices, then $(AB-BA)^2$ commutes with all $2\times2$ matrices.

What does "Consider R as an vector space over Q" mean?

Find all $n$ by $n$ matrices $A$ such that $A^2 = A.$ [duplicate]

Let $f_n(x)$ be a sequence of integrable functions such that $\lim_{n\to \infty} \int^a_b |f_n(x)|dx=0$. Prove the following

Let $S$ be a linearly dependent set. Then, for each $x$ in $S$, is it true that $x$ is in $\operatorname{span}(S\setminus \{x\})$?

$A$ , an $n\times n$ matrix has $k$ distinct eigenvalues, then the matrix $A^m$ for some $m>=0$ has the same eigenvalues raised to $m$

Prove that the series with terms $a_n$ diverges. [duplicate]

Method for evaluating Darboux integrals by a sequence of partitions?

Can one apply LHopitals' rule to differentiable functions defined over the naturals?

Prove that the product of all the positive divisors of two numbers is equal implies the numbers themselves are equal.

Why does every Laurent Series have a singular point on the outer and inner boundary

Two random variables $U$, $V$ such that the conditional distribution of $U$ given $V = v$ is $ve^{-u}$ for $u > ln(v)$. Prove the following:

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex [duplicate]

Application of the cyclic decomposition theorem to a linear transformation