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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
Using the Karhunen-Loève expansion
() () ) () ( √ 3b)
The coefficients are uncorrelated. We check this by look...
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