Linear Spaces and Transformations

Norman Schofield
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Norman Schofield: Washington University in Saint Louis

Chapter 2 in Mathematical Methods in Economics and Social Choice, 2014, pp 39-75 from Springer

Abstract: Abstract Chapter 2 surveys material on linear or vector spaces, and introduces the idea of a linear transformation between vector spaces, and shows how a linear transformation can be represented by a matrix. We also prove the dimension theorem, which shows how a linear transformation can be represented in a simple form, given by its kernel and image. We also introduce the notion of an eigenvalue and eigenvector of a matrix.

Keywords: Single Linear Transformation; Dimension Theorem; Vector Space; Linear Independence; Remaining Column Vectors (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-642-39818-6_2

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DOI: 10.1007/978-3-642-39818-6_2

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