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) &lt;v,v&gt;\ge 0\/itex] and &amp;lt;v,v&amp;gt;= 0 if and only if v= 0.<br /> 2) &amp;lt;au+ bv,w&amp;gt;= a&amp;lt;u,w&amp;gt;+ b&amp;lt;v,w&amp;gt;.<br /> 3) &amp;lt;u,v&amp;gt;= \overline{&amp;lt;v,u&amp;gt;}}.<br /> (that overline is complex conjugate)<br /> <br /> 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 <b>an</b> 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.