abstract algebra - Why are two permutations conjugate iff they …
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Is the inverse of a symmetric matrix also symmetric?
All the proofs here use algebraic manipulations. But I think it may be more illuminating to think of a symmetric matrix as representing an operator consisting of a rotation, an anisotropic scaling …
Does $\\pi$ contain all possible number combinations?
2012年10月19日 · It is not true that an infinite, non-repeating decimal must contain ‘every possible number combination’. The decimal $0.011000111100000111111\dots$ is an easy counterex
What is conjugate in group theory? - Mathematics Stack Exchange
2016年10月17日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
How do you prove that $tr(B^{T} A )$ is a inner product?
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Conjugate permutations in $S_n$ and / or $A_n$
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
How to prove $\\text{Rank}(AB)\\leq \\min(\\text{Rank}(A), …
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
abstract algebra - For $G$ group and $H$ subgroup of finite index ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
How to prove $\\operatorname{Tr}(AB) = \\operatorname{Tr}(BA)$?
2015年1月11日 · The efficient @hjhjhj57: answer $$\text{Tr}(AB) = \text{Tr}(BA)= \sum a_{ij} b_{ji}$$ Now we can start to understand why if we do a circular permutation of the factors the …
Is positive the same as non-negative?
This has lead to the gag among my friends where appending "in the French sense" turns any open condition into a closed one. $\endgroup$ – Willie Wong Commented Jan 21, 2011 at 23:44