Find the eigenvalues and eigenvectors

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Let [Q] be an orthonormal matrix. Show that the squared distance between any two vectors z and y is equal to the squared distance between [Q]z and [Q]y.

Exercise 3.8 (a) Let [K] = 0.75 0.25 l Show that 1 and 1/2 are eigenvalues of [K] and 0.25 0.75. Find the normalized eigenvectors. Express [K] as [QηQ-1], where [η] is diagonal and [Q] is orthonormal.

(b) Let [K∗] = α[K] for real α /= 0. Find the eigenvalues and eigenvectors of [K∗]. Do not use brute force - think!

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909649

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