Projection Example 1

>> X = [[1;2;3],[1;0;1]]
X =

   1   1
   2   0
   3   1

>> PX = X * (X' * X)^(-1) * X'
PX =

   0.66667  -0.33333   0.33333
  -0.33333   0.66667   0.33333
   0.33333   0.33333   0.66667

>> y = [2;4;6]
y =

   2
   4
   6

>> yX = PX * y
yX =

   2.0000
   4.0000
   6.0000

Since y in this example already lies in the column-space of X, orthogonal projection onto that space has no effect.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.