MAT223H1 Chapter Notes - Chapter 4.2: Vandermonde Matrix
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By de nition, every s s can be written as a linear com- bination of the vectors u1, . + rmum for a given selection of scalars r1, r2, . Note that it is possible that the set(cid:8)u1, . , um (cid:9) to be lin- early dependent. On that case, those vectors that can be written as linear combinations of other can be removed without having an effect on s. This idea of removing linearly dependent elements until, all the remaining vectors are linearly independent has a special name. 1 (basis). (cid:9) is a basis for a subspace s if. , um (a) b spans s. (b) b is linearly independent. The subspace s =(cid:8)0(cid:9) = span(cid:8)0(cid:9) is the only space that has no. , um (cid:9) be a basis for a subspace s. then, every basis. 1. vector s s can be written as a linear combination s = s1u1 + .
