Let T be a self-adjoint operator on a finite-dimensional inner product space V. Prove that for all x ∈V||T(x)±ix||2 = ||T(x)||2 + ||x||2. Deduce that T – i| is invertible and that [(T – i|)−1]∗= (T + i|)−1.
Let T be a self-adjoint operator on a finite-dimensional inner product space V. Prove that for all x ∈V||T(x)±ix||2 = ||T(x)||2 + ||x||2. Deduce that T – i| is invertible and that [(T – i|)−1]∗= (T + i|)−1.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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Let T be a
Deduce that T – i| is invertible and that [(T – i|)−1]∗= (T + i|)−1.
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