Let V be a finite-dimensional inner product space over C with inner product (, ), and let a, b e V \0. Define T : V +V by T(v) = (v, a) b for all v e V. (i) Show that T is a linear map. (ii) For v E V, find T*(v) in terms of v, a, b. (iii) Prove that if T = T*, then b = la for some A E R.
Let V be a finite-dimensional inner product space over C with inner product (, ), and let a, b e V \0. Define T : V +V by T(v) = (v, a) b for all v e V. (i) Show that T is a linear map. (ii) For v E V, find T*(v) in terms of v, a, b. (iii) Prove that if T = T*, then b = la for some A E R.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 71CR: Let V be an inner product space. For a fixed nonzero vector v0 in V, let T:VR be the linear...
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