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These are the first few steps in the proof to demonstrate this: 1. Any vector |y) =Ea;\x'). = (E, Ax)(x') (E", a; x'). 3. LHS: Alu) = A (E a,)x'). 2. Aly) 4. LHS: Al) -Σ4 (A|x')) = Σ4 . i) Justify the operations/assumptions in the first and last lines of this (incomplete) deriva- tion.

These are the first few steps in the proof to demonstrate this: 1. Any vector |y) =Ea;\x'). = (E, Ax)(x') (E", a; x'). 3. LHS: Alu) = A (E a,)x'). 2. Aly) 4. LHS: Al) -Σ4 (A|x')) = Σ4 . i) Justify the operations/assumptions in the first and last lines of this (incomplete) deriva- tion.

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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Do just part i in detail

b) Consider an N × N matrix A with N orthonormal eigenvectors x' such that Ax' = d;x', where the X; is the eigenvalue corresponding to eigenvector x'. In this question you are required to prove that such a matrix A can be written as N N A =EAx*) (x'| =\x'x". i=1 i=1 These are the first few steps in the proof to demonstrate this: 1. Any vector |y) = E1a;|x'). vi=1 = A (E,). 4. LHS: A y) -Σa (Α | x)) = Σ 0, λιx'. 3. LHS: A|y) i) Justify the operations/assumptions in the first and last lines of this (incomplete) deriva- tion.
Transcribed Image Text:b) Consider an N × N matrix A with N orthonormal eigenvectors x' such that Ax' = d;x', where the X; is the eigenvalue corresponding to eigenvector x'. In this question you are required to prove that such a matrix A can be written as N N A =EAx*) (x'| =\x'x". i=1 i=1 These are the first few steps in the proof to demonstrate this: 1. Any vector |y) = E1a;|x'). vi=1 = A (E,). 4. LHS: A y) -Σa (Α | x)) = Σ 0, λιx'. 3. LHS: A|y) i) Justify the operations/assumptions in the first and last lines of this (incomplete) deriva- tion.
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