1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Here's a bit more detail:
    \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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook