User peter

2 votes

1 answer

39 views

Two spaces contain the same vector, can we say the space with smaller dimension is a subspace of the larger one?

linear-algebra functional-analysis

asked Oct 10, 2015 at 6:32

2 votes

3 answers

129 views

How to simply the sum $\sum\limits_{k=1}^n\frac{N-n+k}{(N-k+1)(N-k+1)(N-k)}$?

calculus summation

asked Oct 5, 2016 at 2:44

2 votes

2 answers

83 views

Whether is there a bound of $\sigma^2$ such that $pe^t+qe^{-t}\leq e^{t^2\sigma^2/2}$?

real-analysis

asked Feb 14, 2017 at 23:28

2 votes

1 answer

41 views

How to prove :For $a_i\in(0,1)$ ($i=1,\cdots,N$), then $\prod\limits_{i=1}^Na_i+\prod\limits_{i=1}^N\sqrt{1-a_i^2}\leq1.$

calculus analysis

asked Nov 19, 2015 at 16:48

1 vote

0 answers

34 views

Express the operator of a tensor product by a form containing an inner product term

functional-analysis tensor-products

asked Feb 2, 2016 at 20:25

1 vote

0 answers

22 views

The cardinal number of a net of $l_2$ unit ball in $\mathcal{R}^n$

functional-analysis

asked Jul 5, 2020 at 5:39

1 vote

1 answer

46 views

Is there an upper bound about the probability $\mathcal{P}(\|Ax\|_{\infty}\geq t)$

real-analysis probability functional-analysis analysis probability-theory

asked Mar 4, 2017 at 5:32

1 vote

0 answers

50 views

Is there any clue for the supremum of projective norm in an unit ball of injective tensor product space

functional-analysis tensor-products tensors tensor-rank

asked Oct 24, 2015 at 1:47

1 vote

1 answer

100 views

Is the inner product of matrices invariant under rotation?

linear-algebra

asked Nov 4, 2015 at 16:51

1 vote

3 answers

245 views

Is one projection which preserves norm is identity?

linear-algebra functional-analysis

asked Nov 5, 2015 at 0:42

1 vote

0 answers

239 views

How to prove tensor product of orthogonal projections is still orthogonal ？

abstract-algebra functional-analysis tensor-products

asked Nov 15, 2015 at 22:35

1 vote

0 answers

38 views

Does the following inequality hold? $\sum\limits_{i=1}^a\sum\limits_{j=1}^b\sum\limits_{k=1}^c|A_iB_jC_k|\leq 1$ as $||A||=||B||=||C||=1$

analysis inequality

asked Oct 1, 2015 at 18:31

1 vote

0 answers

58 views

Uniqueness of minimizer of the vector 1-norm of $QM$ over all real orthogonal matrices $Q$

linear-algebra functional-analysis optimization

asked Oct 5, 2015 at 17:20

0 votes

2 answers

33 views

Proof a vector only contains -1, 0 and 1 under condition $\sum\limits_{i=1}^nv_i^2=\sum\limits_{i=1}^n|v_i|$

analysis

asked Oct 1, 2015 at 16:53

0 votes

1 answer

28 views

Whether two matrices $M_1$ and $M_2$ are the same, that their entry-wise sums are the same and $M_2=UM_1V$ , where $U$, $V$ are both othogonal

linear-algebra matrices

asked Oct 1, 2015 at 21:05

0 votes

1 answer

2k views

What is the variance proxy of a such sub-Gaussian random variable

probability probability-theory probability-distributions

asked Jan 22, 2018 at 2:20

0 votes

1 answer

46 views

How to get the number of all possible combinations of k positive integers to reach a given product?

number-theory combinations

asked Jun 2, 2020 at 2:08

0 votes

1 answer

50 views

How to prove $E\|Y'\|\leq E\|Y'-Y''\|,$ where $Y$ is a random matrix in $\mathbb{R}^{n\times n}$, and $Y'$, $Y''$ are independent copies of $Y$?

functional-analysis probability-theory random-matrices

asked Feb 10, 2016 at 2:52

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18 Questions

Two spaces contain the same vector, can we say the space with smaller dimension is a subspace of the larger one?

How to simply the sum $\sum\limits_{k=1}^n\frac{N-n+k}{(N-k+1)(N-k+1)(N-k)}$?

Whether is there a bound of $\sigma^2$ such that $pe^t+qe^{-t}\leq e^{t^2\sigma^2/2}$?

How to prove :For $a_i\in(0,1)$ ($i=1,\cdots,N$), then $\prod\limits_{i=1}^Na_i+\prod\limits_{i=1}^N\sqrt{1-a_i^2}\leq1.$

Express the operator of a tensor product by a form containing an inner product term

The cardinal number of a net of $l_2$ unit ball in $\mathcal{R}^n$

Is there an upper bound about the probability $\mathcal{P}(\|Ax\|_{\infty}\geq t)$

Is there any clue for the supremum of projective norm in an unit ball of injective tensor product space

Is the inner product of matrices invariant under rotation?

Is one projection which preserves norm is identity?

How to prove tensor product of orthogonal projections is still orthogonal ？

Does the following inequality hold? $\sum\limits_{i=1}^a\sum\limits_{j=1}^b\sum\limits_{k=1}^c|A_iB_jC_k|\leq 1$ as $||A||=||B||=||C||=1$

Uniqueness of minimizer of the vector 1-norm of $QM$ over all real orthogonal matrices $Q$

Proof a vector only contains -1, 0 and 1 under condition $\sum\limits_{i=1}^nv_i^2=\sum\limits_{i=1}^n|v_i|$

Whether two matrices $M_1$ and $M_2$ are the same, that their entry-wise sums are the same and $M_2=UM_1V$ , where $U$, $V$ are both othogonal

What is the variance proxy of a such sub-Gaussian random variable

How to get the number of all possible combinations of k positive integers to reach a given product?

How to prove $E\|Y'\|\leq E\|Y'-Y''\|,$ where $Y$ is a random matrix in $\mathbb{R}^{n\times n}$, and $Y'$, $Y''$ are independent copies of $Y$?