Let f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in C2 | f(x) = x} and V- = {x in C2 | f(x) = -x}. Prove that every x in C2 can be written as x = x+ + x- , where x+ is in V+ and x- is in V- .
Let f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in C2 | f(x) = x} and V- = {x in C2 | f(x) = -x}. Prove that every x in C2 can be written as x = x+ + x- , where x+ is in V+ and x- is in V- .
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 f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in C2 | f(x) = x} and V- = {x in C2 | f(x) = -x}. Prove that every x in C2 can be written as x = x+ + x- , where x+ is in V+ and x- is in V- .
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