The Characteristic Polynomial of Projections
Kate Howell, Rongwei Yang
TL;DR
This paper demonstrates that the characteristic polynomial uniquely identifies pairs of projection matrices under unitary transformations, and explores special cases involving multiple projections.
Contribution
It establishes the characteristic polynomial as a complete invariant for pairs of projections and examines cases with three or more projections.
Findings
Characteristic polynomial uniquely determines pairs of projections
Analysis of special cases with three or more projections
Extension of invariance properties to multiple projections
Abstract
This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research