Replacement

S. N. Afriat
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S. N. Afriat: University of Siena

Chapter 5 in Linear Dependence, 2000, pp 55-66 from Springer

Abstract: Abstract Elements yi,…, yq, in a linear space over a field K, are given as combinations of elements xi,…, xp by the linear dependence table $$\begin{array}{*{20}{c}} {{{y}_{1}} \cdots {{y}_{s}} \cdots {{y}_{q}}} \\ {{{x}_{1}}{{t}_{{r1}}} \cdots {{t}_{{1s}}} \cdots {{t}_{q}}} \\ { \vdots \vdots \cdots \vdots \cdots \vdots } \\ {{{x}_{r}}{{t}_{{rs}}} \cdots {{t}_{{rs}}} \cdots {{t}_{{rq}}}} \\ { \vdots \vdots \cdots \vdots \cdots \vdots } \\ {{{x}_{p}}{{t}_{{p1}}} \cdots {{t}_{{ps}}} \cdots {{t}_{{pq}}}} \\ \end{array}$$ which informs that $${{y}_{j}} = \sum\nolimits_{i} {{{x}_{i}}{{t}_{{ij}}}} ,$$ where $${{t}_{{ij}}} \in K.$$

Date: 2000
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DOI: 10.1007/978-1-4615-4273-5_6

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