hw9 - S,T L ( V ) are linear operators such that S and ST...

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HW # 9 Due date: 4/12/2011 page 159: 11, 13,15,18,22 Hint for 22: Show that 1 or -1 is an eigenvalue of S . Use the structure theorem for isometries. 1. Suppose that S ∈ L ( V ) is an isometry. Using the fact that SS * = I , show that S * is also an isometry. 2. Suppose that S,T ∈ L ( V ) are isometries. Show that ST is an isometry. 3. Suppose that
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Unformatted text preview: S,T L ( V ) are linear operators such that S and ST are isometries. Show that T is also an isometry. 4. Let S L ( V ) and let e 1 ,...,e n be an orthonormal basis of V . Show that S is an isometry i Se 1 ,...,Se n is an orthonormal basis of V. Exam 2 is on April 14th. 1...
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