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7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H.

7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H. (d) Describe the geometric meaning of the linear operator on R" defined by H. (Hint: Com- pute Hu and Hv for any v that is orthogonal to u.)
Transcribed Image Text:7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H. (d) Describe the geometric meaning of the linear operator on R" defined by H. (Hint: Com- pute Hu and Hv for any v that is orthogonal to u.)
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