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Unformatted text preview: X is singular. d. Construct an example in which K X and R X are both singular but μ X 6 = 0. e. Verify that R − 1 X = K − 1 X − K − 1 X μ X μ † X K − 1 X 1 + μ † X K − 1 X μ X . Problem 3. Let X ( u ) be a random vector with correlation matrix R X . Let e 1 and e 2 be eigenvectors corresponding to distinct eigenvalues λ 1 and λ 2 , respectively. Assume that  e 1  =  e 2  = 1 . Let Y i ( u ) = e † i X ( u ) , i = 1 , 2 . 1 a. Compute E [  Y 1 ( u )  2 ]. b. Compute E [ Y 1 ( u ) Y 2 ( u ) ∗ ]. 2...
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 Summer '07
 ToddBrun
 Linear Algebra, Eigenvalue, eigenvector and eigenspace, kx, covariance matrix Kx

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