Orthogonal Projections vs Non-orthogonal projections?

  • Thread starter rayzhu52
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  • #1
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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!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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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