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Unit 24: Orthogonal Complements
4. If S is a non-empty subset of a Hilbert space H, show that S is the closure of the set of all Notes
linear combinations of vectors in S.
5. If M and N are closed linear subspace of a Hilbert space h such that M N, then the linear
subspace M + N is closed.
24.5 Further Readings
Books Halmos, Paul R. (1974), Finite-dimensional Vector Spaces, Berlin, New York
Paul Richard Halmos, A Hilbert Space Problem Book, 2nd Ed.
Online links Itcconline.net/green/courses/203/…/orthogonal complements.html
www.math.cornell.edu/~andreim/Lec33.pdf
www.amazon.co.uk
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