A row module for a matrix algebra A is a row space over a field F on that A acts from the right via matrix multiplication. All operations, set theoretic functions and vector space functions for row spaces are applicable to row modules, and the conventions for row spaces also hold for row modules (see chapter Row Spaces). For the notion of a standard basis of a module, see StandardBasis for Row Modules.
It should be mentioned, however, that the functions and their results have to
be interpreted in the module context. For example,
Generators returns a
AsSpace for Modules), and
Sum for modules return a module (namely the
smallest module generated by the arguments).
Quotient modules Q = V / W of row modules are quotients of row spaces V, W that are both (row) modules for the same matrix algebra A. All operations and functions for quotient spaces are applicable. The element of such quotient modules are module cosets, in addition to the operations and functions for row space cosets they can be multiplied by elements of the acting algebra.
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