MATH 4389 Study Guide - Final Guide: Vector Space, Row And Column Spaces, Null Character
19 Apr 2017
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Definition: a vector space is a nonempty set v of objects, called vectors, together with vector addition and scalar multiplication satisfying: (cid:1) Such that u u (cid:1) Let h be a nonempty subset of v . H is said to be a subspace of v if: the zero vector is in h , h is closed under vector addition. That is: h is closed under scalar multiplication. Examples: the set {{{{ }}}}0 (cid:1) is a subspace of v; it is called the zero subspace, subspaces of. 2: let p be the set of all polynomials with real coefficients. ( p is a subset of the vector space of all real valued functions defined on . ) Let q be the set of all polynomials with degree 2 . 2,v v v and v are vectors in v , then p v v. }p v v . p is called the subspace spanned (or generated) by the.
