4.3: Linearly Independent Sets; Bases flash cards

Set: 4.3: Linearly Independent Sets; Bases

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Term	Definition
linearly independent set of vectors {v1,..., vp} in V	the vector equation c1v1 + c2v2 + .. + cpvp = 0 has only the trivial solution c1 =0, ..., cp=0
basis for subspace H of vector space V	an indexed set of vectors (Beta) = {b1, ..., bp} such that a. (Beta) is a linearly independent set and b. the subspace spanned by (Beta) coincides with H; that is, H = Span {b1, ..., bp}; applies when H = V; an efficient spanning set that contains no unnecessary vector
standard basis for R^n	the set {e1, ..., en} composed of the columns of the n x n identity matrix In
standard basis for Pn	S = {1, t, t^2, ... t^n}