Geodesic
Invertion of infinite Gaussian matrices
Matematičeskie zametki SVFU, Tome 25 (2018) no. 3, pp. 54-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study existence of the left inverse, right inverse and inverse of Gaussian infinite matrices (those are the upper infinite triangular matrices with nonzero elements on the main diagonal). The existence of a unique inverse of the Gaussian matrix is proved. Also, an explicit expression for the inverse of the Gaussian matrix of any order is found, including the infinite case. Implementation of this expression is very convenient, since calculations are based on recurrence relations. Such approach can be extended to triangular infinite matrices (those are the lower infinite triangular matrices with nonzero elements on the main diagonal). Thus, there is the possibility of inversion of an infinite matrix of infinite rank, since such matrices decompose into the product of two matrices, a triangular and a Gaussian.
Keywords: infinite system, linear algebraic equation, infinite triangular matrix, infinite determinant.
Mots-clés : Gaussian matrix, inverse matrix 
@article{SVFU_2018_25_3_a4,
     author = {F. M. Fedorov and N. N. Pavlov and S. V. Potapova and O. F. Ivanova},
     title = {Invertion of infinite {Gaussian} matrices},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {54--67},
     year = {2018},
     volume = {25},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2018_25_3_a4/}
}
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F. M. Fedorov; N. N. Pavlov; S. V. Potapova; O. F. Ivanova. Invertion of infinite Gaussian matrices. Matematičeskie zametki SVFU, Tome 25 (2018) no. 3, pp. 54-67. http://geodesic.mathdoc.fr/item/SVFU_2018_25_3_a4/