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user1551
  • Member for 13 years, 9 months
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58 votes
9 answers
8k views

On the functional square root of $x^2+1$

42 votes
18 answers
2k views

$2\times2$ matrices are not big enough

31 votes
2 answers
7k views

Etymology of the word "normal" (perpendicular)

13 votes
2 answers
2k views

Do determinants of binary matrices form a set of consecutive numbers?

11 votes
1 answer
8k views

Eigenvalues of the principal submatrix of a Hermitian matrix

11 votes
2 answers
690 views

If the entries of a positive semidefinite matrix shrink individually, will the operator norm always decrease?

8 votes
5 answers
1k views

The longer the base, the longer the hypotenuse

8 votes
4 answers
2k views

Is $\tan\theta\cos\theta=\sin\theta$ an identity?

7 votes
6 answers
322 views

Intuitive proof of $\frac{1+e^x}2>\frac{e^x-1}x$ for high school students

6 votes
1 answer
207 views

It is not always possible to express two diagonal matrices as polynomials of some matrix

6 votes
1 answer
303 views

A $3\times3$ triangular matrix has a repeated eigenvalue if it is the square of a non-triangular matrix

6 votes
1 answer
215 views

Proofs of Karpelevich's results about eigenvalues of nonnegative matrices.

5 votes
1 answer
289 views

If $A,B,C$ are nonsingular, so is $A\sin(t)+B\cos(t)+C$ for some real $t$

5 votes
0 answers
279 views

Maximum element of Perron vector

4 votes
2 answers
380 views

"Etymology" of symbols for injections and surjections

4 votes
1 answer
109 views

Does the cross section of $[-1,1]^n$ on a $k$-dimensional subspace always contains a rotated image of $[-1,1]^k$?

3 votes
1 answer
143 views

What does an entire function whose images are normal matrices look like?

3 votes
1 answer
227 views

If a linear isometry is injective on a subset of $\mathbb R^n$, is it also surjective?

1 vote
1 answer
71 views

Does there exist a singular $3\times3$ stochastic matrix $A$ such that $a_{ii}>\max(a_{ij},a_{ji})$ for all $i\ne j$?

0 votes
1 answer
128 views

Book on bogus proofs or counterexamples in plane geometry