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visits member for 3 years, 8 months
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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)?
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
edited title
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
edited title
Oct
17
comment How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
A non-pythagorean question is added.
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
added 79 characters in body
Oct
17
revised How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
added 79 characters in body
Oct
17
comment How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?
Ah, $(a^2-b^2)^2+(2ab)^2=(a^2+b^2)^2$. So I have to find all $(a,b)$'s such that $a^2+b^2=2m$.
Oct
17
comment Solution to a system of linear equations in GF(2)
An insightful answer. It is brilliant to consider $A^2$. To solve the puzzle I have to handle all the cases so I give the "√" to @user1551, but this is impressive.
Oct
17
comment Solution to a system of linear equations in GF(2)
Thank you, @user1551. Actually the question is from a variant of lights out puzzle, where the light pressed affects the whole row and column.
Oct
17
asked How many $n$'s can make $4m^2-n^2$ a perfect square? And, triple of a perfect square?