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Let e1, e2,..., en be an orthonormal list of vectors in an inner product space V over F. For any choice of a1,..., an E F, show that aje, and aze2+.+anen are orthogonal. (This result is needed for the proof of Result 6.25.)

Let e1, e2,..., en be an orthonormal list of vectors in an inner product space V over F. For any choice of a1,..., an E F, show that aje, and aze2+.+anen are orthogonal. (This result is needed for the proof of Result 6.25.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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Let e1, e2,..., en be an orthonormal list of vectors in an inner product space V over F. For any choice of a1,..., an E F, show that aje, and aze2+.+anen are orthogonal. (This result is needed for the proof of Result 6.25.)
Transcribed Image Text:Let e1, e2,..., en be an orthonormal list of vectors in an inner product space V over F. For any choice of a1,..., an E F, show that aje, and aze2+.+anen are orthogonal. (This result is needed for the proof of Result 6.25.)
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