Consider the vector space C2 with the standard inner product. Define the linear operator T:C? → C2 by T(x, y) = (2x+iy, (1– i)x). Find T* (3 - i,1+2i) where T* is the adjoint of T. Is T normal?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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Consider the vector space C2 with the standard inner product. Define the linear operator
T:C? → C2 by T(x, y) = (2x + iy, (1–i)x). Find T* (3 – i,1+ 2i) where T* is the adjoint
of T. Is T normal?
Transcribed Image Text:Consider the vector space C2 with the standard inner product. Define the linear operator T:C? → C2 by T(x, y) = (2x + iy, (1–i)x). Find T* (3 – i,1+ 2i) where T* is the adjoint of T. Is T normal?
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