Unformatted text preview: = Span(1 , x , x 2 ) deﬁned by φ ( f ) = f (1), ﬁnd g ∈ W such that φ ( f ) = < f,g > for all f ∈ W . 4. Let V = C n × n with the inner product < X,Y > = tr(X Y t ) and let T be the linear operator on V deﬁned by T ( X ) = • 1 ii 1 ‚ XX • 1 ii 1 ‚ . (a) Show that T is selfadjoint. (b) Find an orthonormal basis of V consisting of eigenvectors of T . Hint: Use the fact that Im(T) ⊥ = Ker(T). (c) Find the matrix A of T with respect to the standard basis of V and ﬁnd a unitary matrix U such that U1 AU is a diagonal matrix....
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 Winter '06
 TOTH
 Linear Algebra, Algebra, Scalar, inner product, McGill University, McGill University Math

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