6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = -Ĵa cos(xt) f(t) dt. Show that (i) T is self-adjoint. (ii) cos x and sin x are eigenvectors of T.
6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = -Ĵa cos(xt) f(t) dt. Show that (i) T is self-adjoint. (ii) cos x and sin x are eigenvectors of T.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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