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Linear Algebra pp 247-271 | Cite as

Complex Vector Spaces

  • Jin Ho Kwak
  • Sungpyo Hong

Abstract

So far, we have been dealing with matrices having only real entries and vector spaces with real scalars. Also , in any system of linear (difference or differential) equations, we assumed that the coefficients of an equation are all real. However, for many applications of linear algebra, it is desirable to extend the scalars to complex numbers. For example, by allowing complex scalars, any polynomial of degree n (even with complex coefficients) has n complex roots counting multiplicity. (This is well known as the fundamental theorem of algebra). By applying it to a characteristic polynomial of a matrix, one can say that all the square matrices of order n will have n eigenvalues counting multiplicity.

Keywords

Orthonormal Basis Triangular Matrix Orthogonal Matrix Real Eigenvalue Hermitian Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Jin Ho Kwak
    • 1
  • Sungpyo Hong
    • 1
  1. 1.Department of MathematicsPohang University of Science and TechnologyPohang, KyungbukSouth Korea

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