Characterization of Orthogonal Projectors
Achiles Nyongesa Simiyu, Alwanyi Kevin Shilaviga, Olege Fanuel
Journal of Advances in Mathematics and Computer Science · pp. 33–42 · Published 29 Apr 2022
10.9734/jamcs/2022/v37i330440Abstract
Let H be a Hilbert space and M be a closed linear subspace of H. Then by projection theorem H = M ⊕ M ⊥ . This theorem suggests that the result has something to do about a notion in Hilbert spaces which is analogous to and a generalization of the familiar idea of Orthogonal or perpendicular projection of a vector in R2 or R3 upon a linear subspace of R2 or R3 respectively. In this paper we give a complete operator characterization of orthogonal projections.Specifically we show that P is an orthogonal projector onto RP = M if and only if P is self-adjoint and idempotent. We also consider the algebraic formulation of invariance, reduction, orthocomplementation and orthogonality.
References (8)
- 1 Linear algebra and its applications [DOI]
- 2 Linear Operators and their Spectra [DOI]
- 3 Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition [DOI]
- 4 Introduction to Hilbert Space. [DOI]
- 5 Spectral Theory of Operators on Hilbert Spaces [DOI]
- 6 Spectral Theory of Operators in Hilbert Space [DOI]
- 7 A property of orthogonal projectors [DOI]
- 8 Orthogonal Projections [DOI]
Cited by 3
Hillary Amonyela Isabu, Kevin Alwanyi Shilaviga, Violet Agala Khaveri · Science Mundi · 2026
Showing 1 of 3 known citations — external sources report more than can currently be individually listed.
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