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Jun
5
comment Cauchy–Schwarz inequality for complex numbers
Should be $\mathrm{Re}(z_1\cdot\bar{z_2})^2\le|z_1|^2|z_2|^2$.
May
17
awarded  Yearling
Apr
25
comment Need help solving Recursive series defined by $x_1 = \sin x_0$ and $x_{n+1} = \sin x_n$
@MaoYiyi As an alternative, it is easy to show that $0<x_{n+1}<x_n<x_1\le 1$, thus $\{x_n\}$ has a limit, which is the solution of $x=\sin x\,(0<x<1)$.
Apr
24
comment Proof $||A||_{p} < 1 \Rightarrow \lim\limits_{k \rightarrow \infty}{A^k} = 0$ for any $A \in \mathbb R^{n \times n}$
Hint: $\|AB\|\le\|A\|\|B\|$ for all $p$-norm.
Apr
23
comment Proving that an $n\times n$ matrix has at most $n$ distinct eigenvalues
If $F$ is algebraically close, the equation will have $n$ roots, otherwise, less than $n$.
Apr
23
comment Need help solving Recursive series defined by $x_1 = \sin x_0$ and $x_{n+1} = \sin x_n$
@MaoYiyi , if you are confused, try to take $x_1$ as the start value.
Apr
23
answered Need help solving Recursive series defined by $x_1 = \sin x_0$ and $x_{n+1} = \sin x_n$
Apr
19
suggested suggested edit on Show that $\int_{-\pi}^{\pi}e^{\alpha \cos t}\sin(\alpha \sin t)dt=0$
Apr
19
accepted Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
Apr
19
comment Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
I think I understand, thank you, @zyx .
Apr
18
comment How to prove $\sum_{i,j}y_{i}^{T}y_{j} W_{i,j}=tr(Y^{T}WY)$
Isn't it $=\mathrm{tr}Y^TLY$, where $L$ is the Laplacian matrix (en.wikipedia.org/wiki/Laplacian_matrix)?
Apr
15
comment Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
Why won't the "chain" of $A^i$ terminate before $i$ reaches $n$ in the triangle case? I mean, why is it impossible that there exist a $k<n$ such that $A^k=0$?
Apr
15
revised Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
added 33 characters in body
Apr
15
comment Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
Can you give more words on "The similarity type of $N$ is determined by the dimensions of the kernels of powers of $N$"?
Apr
14
revised Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
added 359 characters in body
Apr
14
revised Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
added 306 characters in body
Apr
14
revised Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
added 271 characters in body
Apr
14
asked Similarity between $I+N$ and $e^N$ when $N$ is nilpotent
Oct
18
accepted How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
Oct
18
comment How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
Thank you, @André Nicolas, it's a nice answer and reference. Is there literature on decomposing an integer into a perfect square and a prime multiple of another perfect square (Just as the second part of the question)?