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Linear Spaces and Transformations

In: Mathematical Methods in Economics and Social Choice

Author

Listed:
  • Norman Schofield

    (Washington University in Saint Louis)

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.

Suggested Citation

  • Norman Schofield, 2014. "Linear Spaces and Transformations," Springer Texts in Business and Economics, in: Mathematical Methods in Economics and Social Choice, edition 2, chapter 2, pages 39-75, Springer.
    • Handle: RePEc:spr:sptchp:978-3-642-39818-6_2
    DOI: 10.1007/978-3-642-39818-6_2
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