The many proofs of an identity on the norm of oblique projections | Zendy

Daniel B. Szyld | Zendy

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The many proofs of an identity on the norm of oblique projections

Author(s) -

Daniel B. Szyld

Publication year - 2006

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/s11075-006-9046-2

Subject(s) - mathematics , mathematical proof , theory of computation , hilbert space , oblique case , norm (philosophy) , identity (music) , algebra over a field , pure mathematics , calculus (dental) , algorithm , geometry , epistemology , linguistics , dentistry , acoustics , medicine , philosophy , physics

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P 2=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.

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