Chapter

The Fundamental Theorem of Linear Algebra

Gidon Eshel

in Spatiotemporal Data Analysis

Published by Princeton University Press

Published in print December 2011 | ISBN: 9780691128917
Published online October 2017 | e-ISBN: 9781400840632
The Fundamental Theorem of Linear Algebra

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This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices, vectors, and their interactions. To make the discussion helpful and informal yet rigorous, and to complement the slightly more formal introduction of the basic ideas given in an earlier chapter, here the theorem’s pictorial representation is emphasized. The discussions cover the forward problem, when A ɛ ℝM×N maps an x ɛ ℝN from A’s domain onto b ɛ ℝM in A’s range, how A transforms x into b; and the inverse problem, discussed in detail in chapter 9, section 9.4.1.

Keywords: linear algebra; matrices; vectors; forward problem; inverse problem

Chapter.  1119 words.  Illustrated.

Subjects: Social Impact of Environmental Issues (Social Science)

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