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Matrix Eigenvalues

  • Sujit Kumar BoseEmail author
Chapter
  • 913 Downloads
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Abstract

Given an \(n\times n\) (real or complex) matrix A and an n-vector \(\mathbf{x}\), suppose we construct the n-vector \(A\mathbf{x}=:\mathbf{y}\), then A can be interpreted as a linear transformation which carries \(\mathbf{x}\) to \(\mathbf{y}\) in an n-dimensional space. In particular, if a non-zero vector \(\mathbf{x}\) can be found such that A carries \(\mathbf{x}\) to a collinear vector \(\lambda \mathbf{x}\), i.e.
$$A\mathbf{x}=\lambda \mathbf{x}$$
then \(\mathbf{x}\) is called an eigenvector of A and \(\lambda \) its corresponding eigenvalue.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.S. N. Bose National Centre for Basic SciencesKolkataIndia

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