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The covariance-variance matrix of a set of observations, Exx, is a symmetric matrix. The covariance matrix of functions of these observations should also be symmetric as the two covariance matrices are related by the equation Eyy= JEXXJT. Using laws on matrix transposition, prove that, indeed, Eyy is symmetric by showing that the product JEXXJT is symmetric, i.e., the original product and its transpose are equal. You need to list the transposition law concerned, or a property of a matrix, at every step of the proof.

The covariance-variance matrix of a set of observations, Exx, is a symmetric matrix. The covariance matrix of functions of these observations should also be symmetric as the two covariance matrices are related by the equation Eyy= JEXXJT. Using laws on matrix transposition, prove that, indeed, Eyy is symmetric by showing that the product JEXXJT is symmetric, i.e., the original product and its transpose are equal. You need to list the transposition law concerned, or a property of a matrix, at every step of the proof.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 14EQ
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The covariance-variance matrix of a set of observations, xx, is a symmetric matrix. The Covariance matrix of functions of these observations should also be symmetric as the two covariance matrices are related by the equation Eyy= JEXXJT. Using laws on matrix transposition, prove that, indeed, Eyy is symmetric by showing that the product JEXXJT is symmetric, i.e., the original product and its transpose are equal. You need to list the transposition law concerned, or a property of a matrix, at every step of the proof.
Transcribed Image Text:The covariance-variance matrix of a set of observations, xx, is a symmetric matrix. The Covariance matrix of functions of these observations should also be symmetric as the two covariance matrices are related by the equation Eyy= JEXXJT. Using laws on matrix transposition, prove that, indeed, Eyy is symmetric by showing that the product JEXXJT is symmetric, i.e., the original product and its transpose are equal. You need to list the transposition law concerned, or a property of a matrix, at every step of the proof.
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