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glS
  • Member for 9 years, 8 months
  • Last seen this week
  • Europe
65 votes
7 answers
6k views

Is there any geometric intuition for the factorials in Taylor expansions?

14 votes
4 answers
1k views

Is the identity axiom in the definition of group action redundant?

12 votes
1 answer
525 views

Why does representing groups as linear operators provide insight about the groups themselves?

10 votes
1 answer
472 views

What do the level sets of the Shannon entropy look like?

9 votes
3 answers
2k views

Proof of the CS (cosine-sine) matrix decomposition

9 votes
1 answer
2k views

Geometric proof that projections on convex sets are contractive

9 votes
0 answers
253 views

Why does $df\wedge dg$ represent the "density of curves" of constant $f$ and $g$?

8 votes
1 answer
294 views

Do Shannon entropy and majorization preorder measure the same "type of disorder"?

7 votes
4 answers
540 views

The tea bag problem: probability of extracting a single bag of tea

7 votes
3 answers
1k views

Are all square roots of diagonalizable matrices diagonalizable?

7 votes
1 answer
317 views

What is the sum of products of pairs of integers: $\sum_{0\le i<j\le n} ij$?

7 votes
2 answers
1k views

How does the Hopf fibration generalize to maps $S^{2n+1}\to \mathbb{CP}^n$?

7 votes
2 answers
489 views

What do the fibers of the double tangent bundle look like?

6 votes
3 answers
2k views

What is the intuition behind the kernel of $A$ being orthogonal to the range of $A^*$?

6 votes
2 answers
1k views

Why is the spectrum usually defined for operators between Banach spaces?

6 votes
1 answer
713 views

Is there any relation between an eigenvector of $A$ and the eigenvector of $A^T$ with the same eigenvalue?

6 votes
1 answer
949 views

How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?

6 votes
4 answers
852 views

Why does exponentiating group elements by integers always make sense?

6 votes
2 answers
175 views

How do I recover a convex region from the set of its tangent planes?

6 votes
1 answer
410 views

If $A,B$ are diagonalisable, does $AB$ diagonalisable imply $BA$ diagonalisable?

5 votes
1 answer
527 views

Why do partitions correspond to irreps in $S_n$?

5 votes
1 answer
120 views

Why does this trick to derive the formula for $[A^n,B]$ in terms of repeated commutators work so well?

5 votes
1 answer
357 views

What are the singular values of Jordan blocks?

5 votes
1 answer
196 views

Prove that $\det\begin{pmatrix}A&B\\-B&A\end{pmatrix}$ is a sum of squares of polynomials

4 votes
1 answer
77 views

Why is Lie group unimodularity related to the determinant of the adjoint?

4 votes
0 answers
285 views

What is the relation between Fubini-Study metric and the standard metric on hyperspheres?

4 votes
2 answers
188 views

How to parametrise a hyperplane without making assumptions on the coefficients of its normal vector?

4 votes
1 answer
626 views

Why is the Legendre transform (of vector bundles) a smooth morphism $\mathbf FL:E\to E^*$?

4 votes
0 answers
52 views

Is finding the (multiplicative) inverse of an element in a field always easy?

4 votes
5 answers
257 views

Evaluation of $\lim_{x \to k\pi} \frac{\sin(x)}{x(x-k\pi)}$ from the Weierstrass product expansion of $\sin(x)$

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