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comment Can I represent groups geometrically?
Many groups have an inherent geometric interpretation, such as the dihedral groups, the symmetry groups of the archimedean solids and wallpaper groups. Also, see Cayley graph.
Apr
24
comment Understanding Maximum Principle
Local (almost) always means open neighbourhoods.
Apr
24
revised How to find high power numbers modulo
added 16 characters in body
Apr
24
comment Understanding Maximum Principle
A little bit outside your context, but I think it illustrates your last question better than a more correct example: if you have the function $f:\Bbb R \to \Bbb R$ given by $f(x) = x$, and the open, bounded set $U = (0, 1) \subseteq \Bbb R$, then $f$ has no maxima or minima at all on $U$.
Apr
24
answered How many elements are there in the vector space over F of dimension 5
Apr
23
comment Under what condition does $A^T(B \times C) + (B\times C)^T A = 2A^T(B \times C)$, A,B,C vectors
Any $1\times1$ matrix is diagonal, and thus symmetric.
Apr
23
comment How to prove the group of automorphisms of $S^1$ as a topological group is $\mathbb Z_2$?
You could probably use induction to show that those are the only choices for the subgroup $$\left\{z\in S^1\mid \arg(z)=\frac{2\pi}{2^n},n\in \Bbb N\right\},$$and then use continuity to prove it for the rest of the points.
Apr
23
comment Suppose $p$ is a polynomial with real coefficients. Then which of the following statements are necessarily true?
@Arpan My polynomial has the added benefit of roots that does not require nested square roots to express.
Apr
23
comment Suppose $p$ is a polynomial with real coefficients. Then which of the following statements are necessarily true?
$x^4 - 3x^2 -4 = (x-2)(x+2)(x^2 + 1)$ is a counterexample to the first three points simultaneously.
Apr
23
comment Prove limit exists if and only if left and right limits exist and are equal
Is there a typo in $\lim_{x\to a^+}f(x)=L+\lim_{x\to a^-}f(x)$? Maybe the $+$ was meant to be a $=$?
Apr
22
revised If $BA$ has $-1$ as an eigenvalue, then so does $AB$?
added 174 characters in body
Apr
22
answered If $BA$ has $-1$ as an eigenvalue, then so does $AB$?
Apr
22
answered $f:(2,4)→(1,3)$ where $f(x)=x-[x/2]$ (where $[.]$ is the greatest integer function/floor function),then what will be $f^{-1}(x)$.
Apr
22
comment Probability of a deck of cards
If I draw one card after another until I've drawn $52$ cards, the probability that the four kings are among the cards that I've drawn is $1$. If I only draw $3$ cards, then the probability that I've found all four kings is $0$. How many cards are you drawing?
Apr
22
answered probability of bad watch
Apr
21
comment Linear Transformation : Change of Coordinates
Any basis for $\Bbb R^n$ is always a set with $n$ elements, ordered or not. To call it a basis, it is an additional requirement that they all be linearly independent vectors.
Apr
21
revised Can this be a covariance matrix
added 76 characters in body
Apr
21
revised Statistic Help please …
deleted 4 characters in body
Apr
21
comment Non-trivial group homomorphism from an infinite group to a finite group
Shouldn't the elements be just $0$ or $1$ anyways?
Apr
21
comment Non-trivial group homomorphism from an infinite group to a finite group
What does the $\Bbb R$ mean in $P(n;\Bbb R)$?