The many proofs of an identity on the norm of oblique projections |
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| Authors: | Daniel B. Szyld |
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| Affiliation: | (1) Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA |
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| Abstract: | 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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| Keywords: | idempotent operators oblique projections angle between subspaces gap between subspaces |
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