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10.3 You have a dataset {x} of N vectors, X₁, each of which is d-dimensional. Assume that Covmat ({x}) has one non-zero eigenvalue. Assume that x₁ and x₂ do not have the same value. (a) Show that you can choose a set of t; so that you can represent every data item x; exactly X₁ = X₁ + 1₁(x₂ - X₁). (b) Now consider the dataset of these t values. What is the relationship between (a) std (t) and (b) the non-zero eigenvalue of Covmat ({x})? Why?

10.3 You have a dataset {x} of N vectors, X₁, each of which is d-dimensional. Assume that Covmat ({x}) has one non-zero eigenvalue. Assume that x₁ and x₂ do not have the same value. (a) Show that you can choose a set of t; so that you can represent every data item x; exactly X₁ = X₁ + 1₁(x₂ - X₁). (b) Now consider the dataset of these t values. What is the relationship between (a) std (t) and (b) the non-zero eigenvalue of Covmat ({x})? Why?

MATLAB: An Introduction with Applications
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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10.3 You have a dataset {x} of N vectors, X;, each of which is d-dimensional. Assume that Covmat ({x}) has one non-zero eigenvalue. Assume that X₁ and x2 do not have the same value. (a) Show that you can choose a set of t; so that you can represent every data item x; exactly X₁ = X₁ + ti(x₂ - X1). (b) Now consider the dataset of these t values. What is the relationship between (a) std (t) and (b) the non-zero eigenvalue of Covmat ({x})? Why?
Transcribed Image Text:10.3 You have a dataset {x} of N vectors, X;, each of which is d-dimensional. Assume that Covmat ({x}) has one non-zero eigenvalue. Assume that X₁ and x2 do not have the same value. (a) Show that you can choose a set of t; so that you can represent every data item x; exactly X₁ = X₁ + ti(x₂ - X1). (b) Now consider the dataset of these t values. What is the relationship between (a) std (t) and (b) the non-zero eigenvalue of Covmat ({x})? Why?
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