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Is there a closed form expression for the eigenvectors of a 2x2 matrix?

score 3.3k · Answer 1 · 2026-04-12 11:57:21

3.3k

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Is there a closed form expression for the eigenvectors of a 2x2 matrix?

Published on 12 Apr 2026 - 11:57

score 186 · Answer 2 · 2021-04-15 15:16:05

186

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Prove $\int_{0}^{\pi}\frac{u}{1-\cos u}\ln\frac{1+\sin u}{1-\sin u}{d}u=\left(\pi+2\ln2\right)\pi$

Published on 15 Apr 2021 - 15:16

score 76 · Answer 3 · 2021-04-16 15:26:14

76

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Closed form of $\sum_{n=1}^{\infty} \frac{a^n}{n(n+1)}$

Published on 16 Apr 2021 - 15:26

score 36 · Answer 4 · 2026-04-12 03:01:12

36

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Incomplete upper gamma for a non-integer number of degrees of freedom

Published on 12 Apr 2026 - 3:01

score 65 · Answer 5 · 2021-04-19 22:50:23

65

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Inverse is not connected

Published on 19 Apr 2021 - 22:50

score 336 · Answer 6 · 2026-03-26 22:57:50

336

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How to isolate $x$ in $a^x + b^x = c$? (For use in medical statistics)

Published on 26 Mar 2026 - 22:57

score 53 · Answer 7 · 2021-04-20 17:49:55

53

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Computing $\int_0^1 \frac{(1-t)(1+at)}{|1+at|^p} dt$.

Published on 20 Apr 2021 - 17:49

score 36 · Answer 8 · 2026-04-12 13:41:00

36

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Closed form of some interesting indefinite integrals

Published on 12 Apr 2026 - 13:41

score 131 · Answer 9 · 2021-04-23 22:38:19

131

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How to solve $\cos x = x \sin x$

Published on 23 Apr 2021 - 22:38

score 39 · Answer 10 · 2026-04-11 18:19:05

39

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Closed form for this power series looking like an hypergeometric?

Published on 11 Apr 2026 - 18:19

score 34 · Answer 11 · 2026-04-11 00:58:13

34

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How to express $n$ unknown variables in a system with $n-1$ equations

Published on 11 Apr 2026 - 0:58

score 147 · Answer 12 · 2021-04-27 10:48:05

147

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Does $\int_1^{\infty}\frac{x^2\tan^{-1}(ax)}{x^4+x^2+1}dx$ have closed form?

Published on 27 Apr 2021 - 10:48

score 46 · Answer 13 · 2021-04-27 20:56:58

46

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What can we say about the closed-form solutions of $ x^q - 2x + 1$ for $\def\N{\mathbb{N}} q \in \N^+$?

Published on 27 Apr 2021 - 20:56

score 98 · Answer 14 · 2026-04-12 04:52:44

98

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Is there another formula which generates Pythagoras' triples such that the largest $2$ of the triple differ by $3$?

Published on 12 Apr 2026 - 4:52

score 4.4k · Answer 15 · 2026-04-10 05:04:06

4.4k

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How to evaluate $\sum_{k=3}^{\infty} \frac{\ln (k)}{k^2 - 4}$?

Published on 10 Apr 2026 - 5:04

List Question

Is there a closed form expression for the eigenvectors of a 2x2 matrix?

Prove $\int_{0}^{\pi}\frac{u}{1-\cos u}\ln\frac{1+\sin u}{1-\sin u}{d}u=\left(\pi+2\ln2\right)\pi$

Closed form of $\sum_{n=1}^{\infty} \frac{a^n}{n(n+1)}$

Incomplete upper gamma for a non-integer number of degrees of freedom

Inverse is not connected

How to isolate $x$ in $a^x + b^x = c$? (For use in medical statistics)

Computing $\int_0^1 \frac{(1-t)(1+at)}{|1+at|^p} dt$.

Closed form of some interesting indefinite integrals

How to solve $\cos x = x \sin x$

Closed form for this power series looking like an hypergeometric?

How to express $n$ unknown variables in a system with $n-1$ equations

Does $\int_1^{\infty}\frac{x^2\tan^{-1}(ax)}{x^4+x^2+1}dx$ have closed form?

What can we say about the closed-form solutions of $ x^q - 2x + 1$ for $\def\N{\mathbb{N}} q \in \N^+$?

Is there another formula which generates Pythagoras' triples such that the largest $2$ of the triple differ by $3$?

How to evaluate $\sum_{k=3}^{\infty} \frac{\ln (k)}{k^2 - 4}$?

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