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• W9195718 abstract "This chapter presents the idea of a vector space, highlights few the consequences of the definition, and presents several examples. It explains the properties of vector spaces. Any vector space S has the following properties: (1) the zero vector 0 is unique, (2) for each U in S , − U is unique, (3) 0 U = 0 for every U in S , (4) a 0 = 0 for every scalar a , (5) (−1) U = − U , and (6) if c U = 0, then c = 0 or U = 0. The chapter focuses on subspaces of a vector space and several ideas that are important for the study of vector spaces, such as linear combination of vectors, linear dependence, and linear transformations. A linear transformation from a vector space S to a vector space T is a rule that assigns elements of S to elements of T in a way that preserves vector addition and scalar multiplication. A linear transformation that is one-to-one and onto is called an isomorphism. If L : S → T is an isomorphism, S is said to be isomorphic to T. The chapter also highlights eigenvalues and eigenvectors." @default.
• W9195718 created "2016-06-24" @default.
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• W9195718 date "1972-01-01" @default.
• W9195718 modified "2023-09-27" @default.
• W9195718 title "Vector Spaces and Linear Transformations" @default.
• W9195718 doi "https://doi.org/10.1016/b978-0-12-699050-8.50007-7" @default.
• W9195718 hasPublicationYear "1972" @default.
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