For n-tuples over the algebraic system (R, circle plus, circle times) = (R, max, +), concepts such as linear dependence, space and basis may be defined by analogy with classical linear algebra. Whenever a space is finitely generated, it possesses a basis and all its bases are trivially related and therefore have the same cardinality. However, for any given n > 2, spaces with bases of arbitrary cardinality may be constructed, as well as spaces with no basis. (C) 2004 Elsevier Inc. All rights reserved.
- generating set
- independent set