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Spectral Theory of Compact Self Adjoint Operators

In: Basic Classes of Linear Operators

Author

Listed:
  • 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)

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 $$ A{{\varphi }_{i}} = {{\lambda }_{i}}{{\varphi }_{i}},1 \leqslant i \leqslant n. $$

Suggested Citation

  • Israel Gohberg & Seymour Goldberg & Marinus A. Kaashoek, 2003. "Spectral Theory of Compact Self Adjoint Operators," Springer Books, in: Basic Classes of Linear Operators, chapter 0, pages 171-191, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7980-4_4
    DOI: 10.1007/978-3-0348-7980-4_4
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