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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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