The for distinct eigenvalues otherwise more general

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Unformatted text preview: inct eigenvalues (otherwise more general case is handled by Jordan form) so we have which is what we wanted to show, that the eigenvalues are the diagonal elements of the triangular matrix. Problem 2 First, to show the relationship between the trace and the eigenvalues, we take advantage of the fact that R is diagonalizable () ( ) ( ) () ∑ We also used the property ( ) () The correlation matrix for this problem has the following structure [ Therefore, () ∑ Problem 3 3a) Using the Karhunen-Loève expansion () () ) () ( √ 3b) The coefficients are uncorrelated. We check this by look...
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