Unformatted text preview: Two random vectors X and Y are said to be statistically orthogonal if: Θ XY = 90 ◦ ⇐⇒ E { X T Y } = 0 . In a similar fashion two random vectors X and Y are said to be statistically colinear if: Θ XY = 0 ⇐⇒ E 2 { X T Y } = E { X  2 } E { Y  2 } . When the random vectors are scalars. i.e., 1D random variables these results reduce back to the ones we saw with just two random variables. Any random vector in the sample space has a Karhunen Loeve (KLT) expansion of the form: X = n X i =1 λ i ~v i , where the λ i are the expansion coe±cients and ~v i are the orthonormal eigenvectors of the covariance matrix C X of the random vector X...
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 Fall '11
 GraceGraham
 Linear Algebra, Hilbert space, Cauchy–Schwarz inequality, random vectors

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