= V → R be a lincar map. If Im(T) # {0}:= (01, 02, ..., Un–1) be an orthonormal basis of Ker(T). We can extend Bonormal basis of V by sclecting ĩn appropriately. That is, C = BU{in}..., in-1, Un) is an orthonormal basis of V. Show that T can be expressed(ū, w) for some fixed w e V.

Answered: Image /qna-images/answer/1b364895-53fc-4eb1-b6e6-0275029b3761.jpg

Answered: = V → R be a lincar map. If Im(T) #…

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 S = {1,2,3,4} and U = { ƒ € Fun(S) | ƒ(2) − 3ƒ(4) = 0, ƒ(3) = 0} Find a basis of U. Basis (U) = {} Write your basis using characteristic functions, with x1 for X₁ and x2 for X₂ etc.
11
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6. Let |V(12)) be a state on H") 8 H2). Let {|k)} be an orthonormal basis for H") and {\j)} an orthonormal basis for H2). Show that |V(12)) = Ik) ® (k|V(12)) and
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= V → R be a lincar map. If Im(T) # {0}: = (01, 02, .., n–1) be an orthonormal basis of Ker(T). We can cxtend B onormal basis of V by selecting ūn appropriately. That is, C = BU {ĩn} ..., in–1, Tn) is an orthonormal basis of V. Show that T can be cxpressed (7, w) for some fixed w e V.