Question

Why can't we use the same formula for finding distance between skew lines and parallel lines?

score 122 · Answer 1 · 2026-04-13 23:41:32

122

Views

Why can't we use the same formula for finding distance between skew lines and parallel lines?

Published on 13 Apr 2026 - 23:41

score 45 · Answer 2 · 2026-04-13 03:34:20

45

Views

Geometric interpretation of inner product

Published on 13 Apr 2026 - 3:34

score 62 · Answer 3 · 2026-04-17 14:20:59

62

Views

Let $V$ be a $\mathbb{C}$-vector space and $T: V \rightarrow V$ such that $||T(u)-T(v)||=||u-v||$ and $iT(v)=T(iv)$

Published on 17 Apr 2026 - 14:20

score 84 · Answer 4 · 2026-04-16 13:15:40

84

Views

Prove that if $v\in V$ is such that $\left< T(v),v\right>=0$, then $T(v)=0$.

Published on 16 Apr 2026 - 13:15

score 40 · Answer 5 · 2026-04-14 23:03:10

40

Views

Let $a_{ij}=\left<v_j,v_i \right>$ be for $i,j=1,...,n$. Prove that $A=(a_{ij})$ is a positive matrix.

Published on 14 Apr 2026 - 23:03

score 98 · Answer 6 · 2026-04-17 14:30:14

98

Views

Cross product, Dot product.

Published on 17 Apr 2026 - 14:30

score 165 · Answer 7 · 2026-04-14 01:43:31

165

Views

Given a Riemannian manifold $(M,g)$ and a symmetric $2$-tensor field $h$, what is meant by $\langle\mathrm{Ric},h\rangle_g$?

Published on 14 Apr 2026 - 1:43

score 161 · Answer 8 · 2026-04-15 18:19:12

161

Views

When does a set of vectors positively span $\mathbb{R}^n$?

Published on 15 Apr 2026 - 18:19

score 361 · Answer 9 · 2026-04-16 13:30:01

361

Views

Given the vectors a and b such that a+b and 2a-b are perpendicular and a-b and 4a+b are perpendicular, find the angle between a and b

Published on 16 Apr 2026 - 13:30

score 51 · Answer 10 · 2026-05-11 00:30:32

51

Views

In a $C^*$ algebra, if $A\geq B\geq 0$ then $A^{\frac{1}{2}}\geq B^{\frac{1}{2}}$

Published on 11 May 2026 - 0:30

score 275 · Answer 11 · 2026-04-17 14:32:12

275

Views

Proof that $\langle x , T(x) \rangle = 0$ implies $T(x) = 0$ for a vector space over a complex field.

Published on 17 Apr 2026 - 14:32

score 122 · Answer 12 · 2026-04-14 17:01:41

122

Views

Parallelogram law in L1 space - Did not understand counter-example

Published on 14 Apr 2026 - 17:01

score 33 · Answer 13 · 2026-04-13 21:02:40

33

Views

Inner Product and unitary equivalence

Published on 13 Apr 2026 - 21:02

score 62 · Answer 14 · 2026-04-12 11:44:34

62

Views

Can someone prove to me if this inequality with norms and dot products holds?

Published on 12 Apr 2026 - 11:44

score 58 · Answer 15 · 2026-04-14 03:19:45

58

Views

Show that $a\times (a\times b)=-(a\bullet a)b$

Published on 14 Apr 2026 - 3:19

List Question

Why can't we use the same formula for finding distance between skew lines and parallel lines?

Geometric interpretation of inner product

Let $V$ be a $\mathbb{C}$-vector space and $T: V \rightarrow V$ such that $||T(u)-T(v)||=||u-v||$ and $iT(v)=T(iv)$

Prove that if $v\in V$ is such that $\left< T(v),v\right>=0$, then $T(v)=0$.

Let $a_{ij}=\left<v_j,v_i \right>$ be for $i,j=1,...,n$. Prove that $A=(a_{ij})$ is a positive matrix.

Cross product, Dot product.

Given a Riemannian manifold $(M,g)$ and a symmetric $2$-tensor field $h$, what is meant by $\langle\mathrm{Ric},h\rangle_g$?

When does a set of vectors positively span $\mathbb{R}^n$?

Given the vectors a and b such that a+b and 2a-b are perpendicular and a-b and 4a+b are perpendicular, find the angle between a and b

In a $C^*$ algebra, if $A\geq B\geq 0$ then $A^{\frac{1}{2}}\geq B^{\frac{1}{2}}$

Proof that $\langle x , T(x) \rangle = 0$ implies $T(x) = 0$ for a vector space over a complex field.

Parallelogram law in L1 space - Did not understand counter-example

Inner Product and unitary equivalence

Can someone prove to me if this inequality with norms and dot products holds?

Show that $a\times (a\times b)=-(a\bullet a)b$

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