Abstract
Definition of a linear combination of vectors. Definition of linear dependence and independence. A characterization of linear independence for m vectors in ℝn. (See (19.23) for the definition of rank.) A characterization of linear independence for n vectors in ℝn. (A special case of (18.4).)
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References
All the results on vectors in ℝ n are standard and can be found in any linear algebra text, e.g. Fraleigh and Beauregard (1995) or Lang (1987). For abstract spaces, see Kolmogorov and Fomin (1975), or Royden (1968). For contraction mappings and their application in economic dynamics, see Stokey, Lucas, and Prescott (1989).
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© 2010 Springer-Verlag Berlin Heidelberg
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Sydsæter, K., Strøm, A., Berck, P. (2010). Vectors in ℝ n . Abstract spaces. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_18
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DOI: https://doi.org/10.1007/978-3-540-28518-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
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