Spectral Theory of Compact Self Adjoint Operators

Israel Gohberg (), Seymour Goldberg () and Marinus A. Kaashoek ()
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Israel Gohberg: Tel Aviv University, School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences
Seymour Goldberg: University of Maryland, Department of Mathematics
Marinus A. Kaashoek: Vrije Universiteit Amsterdam, Department of Mathematics and Computer Science

Chapter Chapter IV in Basic Classes of Linear Operators, 2003, pp 171-191 from Springer

Abstract: Abstract One of the fundamental results in linear algebra is the spectral theorem which states that if H is a finite dimensional Hilbert space and A ∈ L(H) is self adjoint, then there exists an orthonormal basis ϕ1,…, ϕ n for H and real numbers λ1,…, λ n such that $$ A{{\varphi }_{i}} = {{\lambda }_{i}}{{\varphi }_{i}},1 \leqslant i \leqslant n. $$

Date: 2003
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DOI: 10.1007/978-3-0348-7980-4_4

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