What Do These Symbols and Scopes Mean in Mathematical Notation?

[transgalactic]

there is a double lines of the absolute value
and
whats that scopes mean(those like breaked [ ])?

http://upload.wikimedia.org/math/e/0/f/e0f97539da9536f1ae5b727d2a7d6dd7.png

http://upload.wikimedia.org/math/a/2/d/a2d420a7e7716e726eb65978f76171e7.png

 

[Diffy]

The double line absolute value is called the norm of a vector. Depending on the field, you might have different definitions. See http://en.wikipedia.org/wiki/Norm_(mathematics )

The second symbol, the brackets, are used to denote the span of two vectors. That is the set of all possible linear combinations of two vectors

 

[transgalactic]

found it
i will try to comprehend this stuff

 

[HallsofIvy]

Caution: <a, b> is also often used to mean the inner product of two vectors. In fact, since you refer to it in connection with ||v||, I would be inclined to suspect that is what is meant: ||v||²= <v, v>.

The inner product on a vector space, V, is a function from $V\times V$ to the underlying field, such that
1) [itex]<v,v>\ge 0\/itex] and $<v,v>= 0$ if and only if v= 0.
2) $<au+ bv,w>= a<u,w>+ b<v,w>$.
3) $<u,v>= \overline{<v,u>}}$.
(that overline is complex conjugate)

If you are given a basis,${e_1, e_2, \cdot\cdot\cdot, \e_n}$ for the vector space, so that two vectors, u and v, can be written $v= a_12_1+ a_2e_2+\cdot\cdot\cdot+ a_ne_n$ and $u= b_1e_1+ b_2e_2+ \cdot\cdot\cdot+ b_ne_n$ then the dot product, $u\cdot v= a_1b_1+ a_2b_2+ \cdot\cdot\cdot+ a_nb_n$ is an inner product.

 

[transgalactic]

so if i have vector a=(x,y,z) b=(s,t,d)

||a||=(x^2 + y^2 +z^2)^0.5

<a,b>=x*s + y*t + z*d

(<a,a>)^0.5 =||a||

is it correct?

 

[HallsofIvy]

Yes.