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Let V be the vector space of all (2 × 2)-matrices. The trace tr(A) ER of a matrix A E V is the sum of the diagonal elements, i.e. Show that the base in V is an ONB tr x (ad) = a + d. b= - (( ) ( ) ( ) ( )) (8 0

Let V be the vector space of all (2 × 2)-matrices. The trace tr(A) ER of a matrix A E V is the sum of the diagonal elements, i.e. Show that the base in V is an ONB tr x (ad) = a + d. b= - (( ) ( ) ( ) ( )) (8 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 30EQ
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Let V be the vector space of all (2 × 2)-matrices. The trace tr(A) E R of a matrix A E V is the sum of the diagonal elements, i.e. Show that the base in V is an ONB tr (a d) = a. = a + d. b= ¹ = (( ) · ( )· ( 9) · ( 9))
Transcribed Image Text:Let V be the vector space of all (2 × 2)-matrices. The trace tr(A) E R of a matrix A E V is the sum of the diagonal elements, i.e. Show that the base in V is an ONB tr (a d) = a. = a + d. b= ¹ = (( ) · ( )· ( 9) · ( 9))
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