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For any two vectors u, v E E such that u v and ||u|| = 12 21 a 17

For any two vectors u, v E E such that u v and ||u|| = 12 21 a 17

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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Let E be any nontrivial Hermitian space. (1) For any two vectors u, v E E such that u ‡ v and ||u|| = ||v||, if u - v = eilu- vl, then the (usual) reflections about the hyperplane orthogonal to the vector v- eu is such that s(u) = eiv. (2) For any nonnull vector v E E, for any unit complex number ei #1, there is a Hermi- tian reflection pv,o such that Pu,o (v) = ev. As a consequence, for u and v as in (1), we have pu,-e o s(u) = = V.
Transcribed Image Text:Let E be any nontrivial Hermitian space. (1) For any two vectors u, v E E such that u ‡ v and ||u|| = ||v||, if u - v = eilu- vl, then the (usual) reflections about the hyperplane orthogonal to the vector v- eu is such that s(u) = eiv. (2) For any nonnull vector v E E, for any unit complex number ei #1, there is a Hermi- tian reflection pv,o such that Pu,o (v) = ev. As a consequence, for u and v as in (1), we have pu,-e o s(u) = = V.
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