Direct Sum of Modules - Direct Sum of Modules With Additional Structure

Direct Sum of Modules With Additional Structure

If the modules we are considering carry some additional structure (e.g. a norm or an inner product), then the direct sum of the modules can often be made to carry this additional structure, as well. In this case, we obtain the coproduct in the appropriate category of all objects carrying the additional structure. Three prominent examples occur for algebras over a field, Banach spaces and Hilbert spaces.

Read more about this topic:  Direct Sum Of Modules

Famous quotes containing the words direct, sum, additional and/or structure:

    It is possible to lead astray an entire generation, to strike it blind, to drive it insane, to direct it towards a false goal. Napoleon proved this.
    Alexander Herzen (1812–1870)

    Lest darkness fall and time fall
    In a long night when learned arteries
    Mounting the ice and sum of barbarous time
    Shall yield, without essence, perfect accident.
    We are the eyelids of defeated caves.
    Allen Tate (1899–1979)

    Don’t you think I’ve had enough excitement for one evening, without the additional thrill of a strange man making love to me?
    John L. Balderston (1899–1954)

    Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other—only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.
    Talcott Parsons (1902–1979)