Idempotency of linear combinations of two idempotent matrices
By J. Baksalary, O. Baksalary. 2000
70 citations recorded by the source corpus.
Abstract A complete solution is established to the problem of characterizing all situations, where a linear combination of two different idempotent matrices P 1 and P 2 is also an idempotent matrix. Including naturally three such situations known in the literature, viz., if the combination is either the sum P 1 + P 2 or one of the differences P 1 − P 2 , P 2 − P 1 (and appropriate additional conditions are fulfilled), the solution asserts that in the particular case where P 1 and P 2 are complex matrices such that P 1 − P 2 is Hermitian, these three situations exhaust the list of all possibilities and that this list extends when the above assumption on P 1 and P 2 is violated. A statistical interpretation of the idempotency problem considered in this note is also pointed out.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/0e9d6e332c53d1b1328fa94a5b71db99ef019f9e
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In Computational Theory and Mathematics
In Electrical and Electronic Engineering
In Numerical Analysis
Citations in the corpus
- A gentle guide to the basics of two projections theory (2010, unknown): “The following result was established in [6].”
- Subspaces, angles and pairs of orthogonal projections (2008, background): “g Baksalary and Baksalary [7,8] investigated the idempotency and nonsingularity of the linear combinations of two oblique projections (see also [32]).”