Geodesic
Products of orthoprojectors and a theorem of Crimmins
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 75-85 
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/
@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/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - Products of orthoprojectors and a theorem of Crimmins
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 75
EP  - 85
VL  - 395
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a7/
LA  - ru
ID  - ZNSL_2011_395_a7
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T Products of orthoprojectors and a theorem of Crimmins
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 75-85
%V 395
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a7/
%G ru
%F ZNSL_2011_395_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 $A^2=AA^*A$.

[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