Anzeige
Erschienen in:
2012 | OriginalPaper | Buchkapitel
5. Linear Independence and Dimension
verfasst von : Prof. Jonathan S. Golan
Erschienen in: The Linear Algebra a Beginning Graduate Student Ought to Know
Verlag: Springer Netherlands
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
The notions of linear independence and bases are defined and studied for arbitrary vector spaces. The notion of dimension is defined. To study bases for arbitrary vector spaces, the Hausdorff Maximum Principle is introduced and used. The properties of finite-dimensional vector spaces are considered. Finally, independence and complements in the lattice of subspaces of a vector space are studied. Among the examples given are the quaternion algebras, Hamel bases, and the complexification of real vector spaces.