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Can someone explain this example ? (Gram-schmidt Orthago

  1. Apr 27, 2012 #1
    http://dl.dropbox.com/u/33103477/4.png [Broken]

    Can someone explain to me how the bits in red are calculated with Integration, the examples are doing my head in and it would be really useful if a human could show me how they are getting the values cause mine are different.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Apr 27, 2012 #2
    For example, the first circle is the integration of t times 1, from 0 to 1, which is equal to [itex]\frac{t^2}{2}|_0^1=\frac{1}{2}[/itex]. The rest are the same
     
  4. Apr 27, 2012 #3

    vela

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    Here's a bit more detail:
    \begin{align*}
    \langle 1, 1 \rangle &= \int_0^1 1\cdot 1 \, dt = t\big|_0^1 = 1 \\
    \langle t, 1 \rangle &= \int_0^1 t\cdot 1 \, dt = \left. \frac{t^2}{2}\right|_0^1 = \frac{1}{2}
    \end{align*} Those are, respectively, the denominator and numerator in the first term you circled.
     
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