Products of orthoprojectors and a theorem of Crimmins
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 75-85
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A proof of the following result, due to T. Crimmins, is proposed: A matrix $A\in M_n(\mathbf C)$ can be represented as a product of orthoprojectors $P$ and $Q$ if and only if $A$ satisfies the equation $A^2=AA^*A$.
@article{ZNSL_2011_395_a7,
author = {Kh. D. Ikramov},
title = {Products of orthoprojectors and a~theorem of {Crimmins}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {75--85},
year = {2011},
volume = {395},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a7/}
}
Kh. D. Ikramov. Products of orthoprojectors and a theorem of Crimmins. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 75-85. http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a7/
[1] G. Corach, A. Maestripieri, “Products of orthogonal projections and polar decompositions”, Linear Algebra Appl., 434 (2011), 1594–1609. | DOI | MR | Zbl
[2] H. Radjavi, J. P. Williams, “Products of self-adjoint operators”, Michigan Math. J., 16 (1969), 177–185 | DOI | MR | Zbl
[3] Y. P. Hong, R. A. Horn, “The Jordan canonical form of a product of a Hermitian and a positive semidefinite matrix”, Linear Algebra Appl., 147 (1991), 373–386 | DOI | MR | Zbl