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Orthogonal Projections vs Non-orthogonal projections?

  1. Dec 3, 2013 #1
    Hi everyone,

    My Linear Algebra Professor recently had a lecture on Orthogonal projections.

    Say for example, we are given the vectors:

    y = [3, -1, 1, 13], v1 = [1, -2, -1, 2] and v2 = [-4, 1, 0, 3]

    To find the projection of y, we first check is the set v1 and v2 are orthogonal:

    v1 • v2 = -4 -2 + 0 + 6 = 0

    So we know the set is orthogonal and we can now find the projection of y, or [itex]\hat{y}[/itex]:

    [itex]\hat{y}[/itex] =[(y • v1)/(v1 • v1) * v1)
    + [(y • v2)/(v2 • v2) * v2)]
    = some value

    Now, we covered what it means when a set is non-orthogonal v1 • vn≠ 0,
    but what if we are asked to find [itex]\hat{y}[/itex]?

    Any form of help would be greatly appreciated!
     
  2. jcsd
  3. Dec 3, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi rayzhu52! :smile:

    (btw, where did you get • from? use . or · (on a mac, it's alt-shift-9))

    (and you've been using too many brackets :wink:)


    the easiest way is probably to start by finding the unit normal, a multiple of v1 x v2 :smile:
     
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