Geodesic
Duality relations connected with Gaussian elimination
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 1, pp. 213-216

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Using the duality relations associated with Gauss's method it is shown that: 1. Any main submatrix of a totally non-degenerate matrix $A$; is stipulated (in the sense of an arbitrary monotonic norm) to be not inferior to $A$; itself; 2. If the inverse of matrix $A$; is diagonally dominant with respect to the columns, then the linear system $Ax=b$ is regularly solved by Jordan's method without the main element being chosen. 
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     author = {Kh. D. Ikramov},
     title = {Duality relations connected with {Gaussian} elimination},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {213--216},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a24/}
}
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Kh. D. Ikramov. Duality relations connected with Gaussian elimination. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 1, pp. 213-216. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a24/