Geodesic
On building matrices in the theory of least squares method
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2019), pp. 27-35.

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct samples of real matrices whose numbers of rows are greater than the number of columns and which satisfy four requirements: the squares of the rows are equal one, the squares of the columns are equal to each other, the columns are pairwise orthogonal, the sum of the components of each column is zero, except for two cases. In the first case, the number of rows is odd, and the number of columns is one. In the second case, the number of rows is odd, and the number of columns is two less than the number of rows. It is proved that in these cases there are no matrices satisfying the four specified requirements. The place of matrices satisfying the four specified requirements is shown in the theory of errors in measuring systems such as GPS.
Keywords: least squares method, minimum of variance, building matrix, duality of building matrices. 
@article{IVM_2019_4_a2,
     author = {O. O. Barabanov and L. P. Barabanova},
     title = {On building matrices in the theory of least squares method},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--35},
     publisher = {mathdoc},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_4_a2/}
}
TY  - JOUR
AU  - O. O. Barabanov
AU  - L. P. Barabanova
TI  - On building matrices in the theory of least squares method
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 27
EP  - 35
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_4_a2/
LA  - ru
ID  - IVM_2019_4_a2
ER  - 
%0 Journal Article
%A O. O. Barabanov
%A L. P. Barabanova
%T On building matrices in the theory of least squares method
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 27-35
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_4_a2/
%G ru
%F IVM_2019_4_a2
O. O. Barabanov; L. P. Barabanova. On building matrices in the theory of least squares method. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2019), pp. 27-35. http://geodesic.mathdoc.fr/item/IVM_2019_4_a2/

[1] Legendre A. M., Nouvelles methode pour la determination des orbites des cometes, Firmin Didot, Paris, 1805, 72–80

[2] Kolmogorov A. N., Petrov A. A., Smirnov Yu. M., “Odna formula Gaussa iz teorii naimenshikh kvadratov”, Izv. AN SSSR. Ser. matem., 11 (1947), 561–566 | MR | Zbl

[3] Maltsev A. I., “Zamechanie k rabote A. N. Kolmogorova, A.A. Petrova, Yu.M. Smirnova (Odna formula Gaussa iz teorii naimenshikh kvadratov)”, Izv. AN SSSR. Ser. matem., 11 (1947), 567–568 | MR | Zbl

[4] Barabanov O. O., Barabanova L. P., Matematicheskie zadachi dalnomernoi navigatsii, Fizmatlit, M., 2007

[5] Barabanova L. P., “K minimizatsii geometricheskikh faktorov GNSS”, Izv. RAN. Teoriya i sistemy upravleniya, 2 (2010), 143–152