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Linear Algebra pp 216-260 | Cite as

Linear mappings of inner product spaces

  • Werner Greub
Part of the Graduate Texts in Mathematics book series (GTM, volume 23)

Abstract

Consider two inner product spaces E and F and assume that a linear mapping (φ:E→ F is given. If E* and F* are two linear spaces dual to E and F respectively, the mapping cp induces a dual mapping φ*:F*→E*. The mappings φ and φ* are related by
$$ < y*,\varphi x > = < \varphi *y*,x > x \in E,y* \in F*$$
(8.1)
.

Keywords

Rotation Angle Orthonormal Basis Linear Transformation Product Space Orthogonal Complement 
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-Verlag New York Inc. 1975

Authors and Affiliations

  • Werner Greub
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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