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)


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
$$ < y*,\varphi x > = < \varphi *y*,x > x \in E,y* \in F*$$


Rotation Angle Orthonormal Basis Linear Transformation Product Space Orthogonal Complement 
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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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