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Demo Recall is on leinen value for t Σ NA & SONS. Then any non-zero UENA is an eigenvector for I of eigen value λ. avail Observation: Suppose V has a basis B={bs, bons such egan b; is an eigenvector for I (of concalve to I Then [T] has ith column [T(b; p = [s; bi] 10= = di [bi]B = diei So [T] B is the diagonal matrive T 2 Terminology: If V has a basis B = {b₁ brs such that [TJB is diagonal. Then we say that I is LT diagonalizble, Th [ T ( ) de b Ex76: I Show that I is diagonalizable if and only if V has a basis conjugation of eigenvections! for To

Demo Recall is on leinen value for t Σ NA & SONS. Then any non-zero UENA is an eigenvector for I of eigen value λ. avail Observation: Suppose V has a basis B={bs, bons such egan b; is an eigenvector for I (of concalve to I Then [T] has ith column [T(b; p = [s; bi] 10= = di [bi]B = diei So [T] B is the diagonal matrive T 2 Terminology: If V has a basis B = {b₁ brs such that [TJB is diagonal. Then we say that I is LT diagonalizble, Th [ T ( ) de b Ex76: I Show that I is diagonalizable if and only if V has a basis conjugation of eigenvections! for To

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 32E
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Demo Recall is on leinen value for t Σ NA & SONS. Then any non-zero UENA is an eigenvector for I of eigen value λ. avail Observation: Suppose V has a basis B={bs, bons such egan b; is an eigenvector for I (of concalve to I Then [T] has ith column [T(b; p = [s; bi] 10= = di [bi]B = diei So [T] B is the diagonal matrive T 2 Terminology: If V has a basis B = {b₁ brs such that [TJB is diagonal. Then we say that I is LT diagonalizble, Th [ T ( ) de b Ex76: I Show that I is diagonalizable if and only if V has a basis conjugation of eigenvections! for To
Transcribed Image Text:Demo Recall is on leinen value for t Σ NA & SONS. Then any non-zero UENA is an eigenvector for I of eigen value λ. avail Observation: Suppose V has a basis B={bs, bons such egan b; is an eigenvector for I (of concalve to I Then [T] has ith column [T(b; p = [s; bi] 10= = di [bi]B = diei So [T] B is the diagonal matrive T 2 Terminology: If V has a basis B = {b₁ brs such that [TJB is diagonal. Then we say that I is LT diagonalizble, Th [ T ( ) de b Ex76: I Show that I is diagonalizable if and only if V has a basis conjugation of eigenvections! for To
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