Geodesic
Factorization of the projection matrix onto a subspace
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 67-76

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A deep factorization of theorthogonal projection matrix onto a subspace is obtained. $LQ$ decomposition isused. For construction of the orthogonal matrix $Q$ the method of successive rankreduction is applied. 
@article{ZNSL_2021_499_a5,
     author = {V. N. Malozemov and G. Sh. Tamasyan},
     title = {Factorization of the projection matrix onto a subspace},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--76},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a5/}
}
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V. N. Malozemov; G. Sh. Tamasyan. Factorization of the projection matrix onto a subspace. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 67-76. http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a5/