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I am learning mathematics to help further mathematical development in my country.


May
19
accepted $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
May
14
awarded  Notable Question
May
12
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers $h$ is just an aribtrary name for the vector. When I used it, I was trying to refer to $v$, to avoid confusion with the $v_n$'s.
May
12
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers I guess I got it. $h$ is the vector $(c_1,c_2,c_3)$. Then I multiply each of it's coordinates for one vector of the basis in order to obtain $v$ which is: $c_1v_1+c_2v_2+c_3v_3$?
May
12
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers Any orthonormal basis is a basis for $\mathbb{R}$? I'm still a little confused because I've read a little about subspaces and there are subspaces that are different of the primary vector space.
May
12
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers I don't understand where are you taking the $c_n$'s from. I'm thinking like this: $v=(v_1,v_2,v_3)$, $v_1=(v_{1,1},v_{1,2},v_{1,3})$, $v_2=(v_{2,1},v_{2,2},v_{2,3})$, $v_3=(v_{3,1},v_{3,2},v_{3,3})$.
May
12
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers I'm still stuck. I've written $\langle v,v_1 \rangle+\langle v,v_2 \rangle + \langle v,v_3 \rangle=0$ but I still can't see it.
May
11
comment What are good questions that could be used to demonstrate the nature of mathematics study?
@PandaBear Yes. Timothy Gowers tried to answer it and the answer was his fabulous 1000 page Princeton Companion to Mathematics.
May
11
asked What are good questions that could be used to demonstrate the nature of mathematics study?
May
10
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers Yes, but there could be also unit vectors that are not perpendicular to each other, isn't it?
May
10
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@T.Bongers The orthonormality of the basis means that the sum of all vectors in the basis equals $1$, right? I've thought only this by summing $(0,1)$ and $(1,0)$ as an example.
May
10
comment $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
@FlybyNight Yes. He's right. Some time later I realized that it's useless to find all the unit vectors.
May
9
awarded  Notable Question
May
8
asked $\mathcal{B}=\{v_1,v_2,v_3\}$ is an orthonormal basis, find all the vectors $v\in \mathbb{R}^3$ such that $\langle v, v_1+v_2-v_3\rangle=0$.
May
5
revised Non-rigorous (maybe a good pop-math) book about real analysis?
added 626 characters in body
May
4
awarded  Nice Question
May
3
awarded  Nice Question
May
3
comment Can you give me some concrete examples of magmas?
@Brad Yes. I've seen in the wikipedia link, it seems to be the most basic structure: One adds the other properties and then one gets the other algebraic structures. But I'm curious specifically about one without associativity, identity, divisibility and comutativity.
May
3
comment Can you give me some concrete examples of magmas?
@MarcinŁoś Now much. But I have a first clue of what they could be. Thanks.
May
3
asked Can you give me some concrete examples of magmas?