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= a Exercise 7.1.23 Let T: C→C be a linear transforma- tion of the real vector space C and assume that T (a) = for every real number a. Show that the following are equivalent: a. T(zw) = T(z)T(w) for all z and w in C. b. Either T = 1c or T(z) = 7 for each z in C (where z denotes the conjugate).

= a Exercise 7.1.23 Let T: C→C be a linear transforma- tion of the real vector space C and assume that T (a) = for every real number a. Show that the following are equivalent: a. T(zw) = T(z)T(w) for all z and w in C. b. Either T = 1c or T(z) = 7 for each z in C (where z denotes the conjugate).

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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= a Exercise 7.1.23 Let T: C→C be a linear transforma- tion of the real vector space C and assume that T (a) = for every real number a. Show that the following are equivalent: a. T(zw) = T(z)T(w) for all z and w in C. b. Either T = 1c or T(z) = 7 for each z in C (where z denotes the conjugate).
Transcribed Image Text:= a Exercise 7.1.23 Let T: C→C be a linear transforma- tion of the real vector space C and assume that T (a) = for every real number a. Show that the following are equivalent: a. T(zw) = T(z)T(w) for all z and w in C. b. Either T = 1c or T(z) = 7 for each z in C (where z denotes the conjugate).
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