Question

Why is the ratio of the $||a-b||_2$ and $||a+b||_2$, $\tan[\angle (a,b)/2]$ when $a$ and $b$ are unit vectors with $a^Tb \geq 0$?

score 43 · Answer 1 · 2026-04-17 05:54:45

43

Views

Why is the ratio of the $||a-b||_2$ and $||a+b||_2$, $\tan[\angle (a,b)/2]$ when $a$ and $b$ are unit vectors with $a^Tb \geq 0$?

Published on 17 Apr 2026 - 5:54

score 40 · Answer 2 · 2026-04-13 22:03:55

40

Views

How to construct a set of vectors orthogonal to other set

Published on 13 Apr 2026 - 22:03

score 103 · Answer 3 · 2026-04-16 08:50:31

103

Views

Consider monic orthogonal polynomials $\{\phi_{0},\phi_{1},\dots,\phi_{n}\}$. Show $||\phi_{k}||\leq||q||$ for all $q \in \Pi_{k}$ with degree $k$

Published on 16 Apr 2026 - 8:50

score 281 · Answer 4 · 2026-04-11 05:56:07

281

Views

Positivity and tensor product

Published on 11 Apr 2026 - 5:56

score 70 · Answer 5 · 2026-04-13 17:49:21

70

Views

Why is this equivalent?

Published on 13 Apr 2026 - 17:49

score 238 · Answer 6 · 2026-04-16 11:53:15

238

Views

If $||u+v||^2=||u||^2+||v||^2$ then $u \perp v$

Published on 16 Apr 2026 - 11:53

score 29 · Answer 7 · 2026-04-09 09:55:33

29

Views

alternate approach to dot product using conjugate

Published on 09 Apr 2026 - 9:55

score 36 · Answer 8 · 2026-04-14 10:38:07

36

Views

If A and B are two given vectors and what is the procedure to find A.▽B and A x ▽B at a given point?

Published on 14 Apr 2026 - 10:38

score 167 · Answer 9 · 2026-04-15 08:50:16

167

Views

Proving T is an isometry if T preserves the norm of the sum of any two orthonormal basis vectors

Published on 15 Apr 2026 - 8:50

score 82 · Answer 10 · 2026-04-15 11:51:20

82

Views

Uniform lower bound of the inner product of two positively correlated random variables

Published on 15 Apr 2026 - 11:51

score 217 · Answer 11 · 2026-04-12 15:58:31

217

Views

What happens when contracting a lightlike with spacelike/timelike vectors?

Published on 12 Apr 2026 - 15:58

score 182 · Answer 12 · 2026-04-14 09:08:04

182

Views

Spectral Theorem for Normal Operators - Help understanding proof

Published on 14 Apr 2026 - 9:08

score 352 · Answer 13 · 2026-04-13 10:38:27

352

Views

Vertex is an extreme point

Published on 13 Apr 2026 - 10:38

score 62 · Answer 14 · 2026-04-15 13:02:49

62

Views

If $A \cap B = \{0\}$ then $A^\perp + B^\perp = V$?

Published on 15 Apr 2026 - 13:02

score 50 · Answer 15 · 2026-04-15 19:08:46

50

Views

What is "n u" and "dv" in this equation?

Published on 15 Apr 2026 - 19:08

List Question

Why is the ratio of the $||a-b||_2$ and $||a+b||_2$, $\tan[\angle (a,b)/2]$ when $a$ and $b$ are unit vectors with $a^Tb \geq 0$?

How to construct a set of vectors orthogonal to other set

Consider monic orthogonal polynomials $\{\phi_{0},\phi_{1},\dots,\phi_{n}\}$. Show $||\phi_{k}||\leq||q||$ for all $q \in \Pi_{k}$ with degree $k$

Positivity and tensor product

Why is this equivalent?

If $||u+v||^2=||u||^2+||v||^2$ then $u \perp v$

alternate approach to dot product using conjugate

If A and B are two given vectors and what is the procedure to find A.▽B and A x ▽B at a given point?

Proving T is an isometry if T preserves the norm of the sum of any two orthonormal basis vectors

Uniform lower bound of the inner product of two positively correlated random variables

What happens when contracting a lightlike with spacelike/timelike vectors?

Spectral Theorem for Normal Operators - Help understanding proof

Vertex is an extreme point

If $A \cap B = \{0\}$ then $A^\perp + B^\perp = V$?

What is "n u" and "dv" in this equation?

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