()--) U1 Let V = C2, and for u = V1 V = E V, define %3| U2 V2 (u, v) = u101 + iujū2 – iuzī1 + 2uzī2. i) Show that this is an inner product on V. ii) Find an orthonormal basis of V with respect to this inner product.
()--) U1 Let V = C2, and for u = V1 V = E V, define %3| U2 V2 (u, v) = u101 + iujū2 – iuzī1 + 2uzī2. i) Show that this is an inner product on V. ii) Find an orthonormal basis of V with respect to this inner product.
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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Transcribed Image Text:()--)
U1
V1
Let V = C², and for u =
E V,
define
V =
U2
V2
(u, v) = u101 + iuj02 – iuzī1 + 2u202.
(i) Show that this is an inner product on V.
(ii) Find an orthonormal basis of V with respect to this inner product.
(iii) Define a linear map T: V → V by
2 0
T(v)
(v E V).
0 1
= Av for all V E V, where T* is the
Find a complex 2 × 2 matrix A such that T*(v)
adjoint of T with respect to the above inner product.
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