Geodesic
Purity And Copurity in Systems of Linear Transformations
Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 889-896

Voir la notice de l'article provenant de la source Cambridge University Press

Consider a system of N linear transformations A1, ... , AN: V → W, where F and IF are complex vector spaces. Denote it for short by (F, W). A pair of subspaces X ⊂ V, Y ⊂ W such that determines a subsystem (X, Y) and a quotient system (V/X, W/Y) (with the induced transformations). The subsystem (X, Y) is of finite codimension in (V, W) if and only if V/X and W / Y are finite-dimensional. It is a direct summand of (V, W) in case there exist supplementary subspaces P of X in F and Q of F in IF such that (P, Q) is a subsystem. 
Zorzitto, Frank. Purity And Copurity in Systems of Linear Transformations. Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 889-896. doi: 10.4153/CJM-1976-086-7
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