Linear mappings of inner product spaces

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))

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In this chapter all linear spaces are assumed to be real and to have finite dimension