Q3. Let x1,..., IN be data in R™ with sample covariance C = XX". Suppose u; is aneigenvector of C corresponding to the eigenvalues A;, with A, 2 2 2 ...Am 2 0. LetP; be the orthogonal projection onto the Span({u;}).(i)Show that the sample variance of P;x1,.., P¿xN is X;.

This question seeks to prove that the sample variance of the projections of a set of data points…

Answered: 00 Q3. Let ₁,...,xN be data in Rm with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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00 Q3. Let ₁,...,xN be data in Rm with sample covariance C = NXXT. Suppose u; is an eigenvector of C corresponding to the eigenvalues A₁, with A₁ A₂ ≥...Am 20. Let P; be the orthogonal projection onto the Span({u;}). (i) Show that the sample variance of Pix,..., PiN is λ₁.