Let V be the space C[-1, 1] with the inner product of Example 7. Find an orthogonal
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Let V be the space C[-1, 1] with the inner product of Example 7. Find an orthogonal basis for the subspace spanned by the polynomials 1, t, and t2. The polynomials in this basis are called Legendre polynomials.
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EXAMPLE 7 For f, g in C[a, b], set (f.g) ·b = = f(t)g(t) dt a Show that (5) defines an inner product on C[a, b]. (5)
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The inner product is fg ftgtdt Then 1 and i are orthogonal because 1 t t dt 0 S...View the full answer
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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