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Homework Help: What these simbols mean?

  1. Nov 21, 2008 #1
  2. jcsd
  3. Nov 21, 2008 #2
    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 [Broken])

    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
     
    Last edited by a moderator: May 3, 2017
  4. Nov 21, 2008 #3
    found it
    i will try to comprehend this stuff
     
    Last edited: Nov 21, 2008
  5. Nov 21, 2008 #4

    HallsofIvy

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

    If you are given a basis,[itex]{e_1, e_2, \cdot\cdot\cdot, \e_n}[/itex] for the vector space, so that two vectors, u and v, can be written [itex]v= a_12_1+ a_2e_2+\cdot\cdot\cdot+ a_ne_n[/itex] and [itex]u= b_1e_1+ b_2e_2+ \cdot\cdot\cdot+ b_ne_n[/itex] then the dot product, [itex]u\cdot v= a_1b_1+ a_2b_2+ \cdot\cdot\cdot+ a_nb_n[/itex] is an inner product.
     
  6. Nov 21, 2008 #5
    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?
     
  7. Nov 21, 2008 #6

    HallsofIvy

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