Question

Let $f:\Bbb R \to\Bbb R^3$ be a differentiable map with $\Vert f(x)\Vert=1$ for any $x \in\Bbb R$. Prove that $f'(x)\cdot f(x)=0.$

score 69 · Answer 1 · 2026-03-25 19:07:11

69

Views

Let $f:\Bbb R \to\Bbb R^3$ be a differentiable map with $\Vert f(x)\Vert=1$ for any $x \in\Bbb R$. Prove that $f'(x)\cdot f(x)=0.$

Published on 25 Mar 2026 - 19:07

score 2.1k · Answer 2 · 2026-03-26 02:54:06

2.1k

Views

If matrix $A$ orthogonal then $A^2$ is orthogonal?

Published on 26 Mar 2026 - 2:54

score 104 · Answer 3 · 2026-03-25 14:25:48

104

Views

Is $Av_1,Av_2,Av_3$ orthogonal if you have eigenvector of $A^TA$

Published on 25 Mar 2026 - 14:25

score 147 · Answer 4 · 2018-09-04 09:25:49

147

Views

Find orthogonal basis for $V^{\perp}$ and find orthogonal projection on $V$.

Published on 04 Sep 2018 - 9:25

score 222 · Answer 5 · 2018-09-04 09:31:00

222

Views

Projection onto the span of linearly independent vectors in Hilbert spaces

Published on 04 Sep 2018 - 9:31

score 59 · Answer 6 · 2026-03-25 14:21:18

59

Views

Optimal orthonormal basis in $\mathbb{R}^p$

Published on 25 Mar 2026 - 14:21

score 34 · Answer 7 · 2018-09-06 05:32:32

34

Views

Finding a base of $S^{\bot}$ is finding a solution for $Ax=0$ but for which matrix?

Published on 06 Sep 2018 - 5:32

score 308 · Answer 8 · 2026-03-25 06:09:47

308

Views

What are examples of ORTHOGONAL function space for multivariable functions?

Published on 25 Mar 2026 - 6:09

score 96 · Answer 9 · 2018-09-06 13:50:22

96

Views

Metric on the space $\lbrace (u,v) \in \mathbb{R}^3\times\mathbb{R}^3 , \langle u,v\rangle=0 \rbrace$

Published on 06 Sep 2018 - 13:50

score 292 · Answer 10 · 2026-03-25 08:07:42

292

Views

Proof: Projection is orthogonal if it is nonexpanding

Published on 25 Mar 2026 - 8:07

score 379 · Answer 11 · 2026-03-25 17:17:17

379

Views

Finding the idempotent matrix

Published on 25 Mar 2026 - 17:17

score 1.5k · Answer 12 · 2026-03-25 08:07:40

1.5k

Views

Proving the uniqueness of a vector projection onto orthogonal complement

Published on 25 Mar 2026 - 8:07

score 558 · Answer 13 · 2026-03-25 22:05:28

558

Views

Does $P$ have to be orthonormal in orthogonal decomposition of a symmetric matrix $A=PDP^T$?

Published on 25 Mar 2026 - 22:05

score 47 · Answer 14 · 2018-09-12 16:57:43

47

Views

Proving orthogonality of factored polynomials

Published on 12 Sep 2018 - 16:57

score 52 · Answer 15 · 2026-03-25 19:05:03

52

Views

Can I use the orthogonality idea from Fourier Series to solve for a simple discrete problem?

Published on 25 Mar 2026 - 19:05

List Question

Let $f:\Bbb R \to\Bbb R^3$ be a differentiable map with $\Vert f(x)\Vert=1$ for any $x \in\Bbb R$. Prove that $f'(x)\cdot f(x)=0.$

If matrix $A$ orthogonal then $A^2$ is orthogonal?

Is $Av_1,Av_2,Av_3$ orthogonal if you have eigenvector of $A^TA$

Find orthogonal basis for $V^{\perp}$ and find orthogonal projection on $V$.

Projection onto the span of linearly independent vectors in Hilbert spaces

Optimal orthonormal basis in $\mathbb{R}^p$

Finding a base of $S^{\bot}$ is finding a solution for $Ax=0$ but for which matrix?

What are examples of ORTHOGONAL function space for multivariable functions?

Metric on the space $\lbrace (u,v) \in \mathbb{R}^3\times\mathbb{R}^3 , \langle u,v\rangle=0 \rbrace$

Proof: Projection is orthogonal if it is nonexpanding

Finding the idempotent matrix

Proving the uniqueness of a vector projection onto orthogonal complement

Does $P$ have to be orthonormal in orthogonal decomposition of a symmetric matrix $A=PDP^T$?

Proving orthogonality of factored polynomials

Can I use the orthogonality idea from Fourier Series to solve for a simple discrete problem?

Trending Questions

Popular # Hahtags

Popular Questions