Let T = L(V) where V is a complex inner product space with the standard innerproduct. DefineT₁=(T+T*), T₂:=1:(T – T*)T(v) =2iand T₁ and T₂ are self-adjoint.(a) Show that T₁T₂ = T₂T₁, then T is normal.(b) Compute T₁ and T₂ when T = L(C²) is given by0-JFind eigenvalues and explain if T is diagonalizable.

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Answered: Let T = L(V) where V is a complex inner…

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 T = L(V) where V is a complex inner product space with the standard inner product. Define T₁ = ² (T+T*), T₂ = (T (T – T*) 2i and T₁ and T₂ are self-adjoint. (a) Show that T₁T₂ = T₂T₁, then T is normal. (b) Compute T₁ and T₂ when T = L(C²) is given by 0 T(v) = [1

Let T = L(V) where V is a complex inner product space with the standard inner product. Define T₁ = ² (T+T), T₂ = (T (T – T) 2i and T₁ and T₂ are self-adjoint. (a) Show that T₁T₂ = T₂T₁, then T is normal. (b) Compute T₁ and T₂ when T = L(C²) is given by 0 T(v) = [1