DLA Terminology and notation

Section 16.2 Terminology and notation

subspace: a subset of vectors in a vector space that itself is a vector space under the same addition and scalar multiplication operations as the parent vector space
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trivial subspace: the subspace of a vector space consisting of only the zero vector
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linear combination (of a collection of vectors $v_{1}, v_{2}, \dots, v_{m}$ ): a vector that can be expressed as
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$k_{1} v_{1} + k_{2} v_{2} + \dots + k_{m} v_{m}$

for some collection of scalars $k_{1}, k_{2}, \dots, k_{m}$
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subspace generated by a set of vectors $S$: the subspace of a vector space consisting of all possible linear combinations of vectors in $S;$ also called the span of $S$ , and written $Span S$
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spanning set (for a vector space): a set of vectors in a vector space (or subspace of a vector space) where the subspace generated by the set is in fact the whole space; could also be called a generating set of vectors for the space
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solution space of homogeneous system $A x = 0$: the subspace of $R^{n}$ (where $n$ is the number of columns of $A$ ) consisting of all solutions to the system
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No results.