Introduction: Notation, Elementary Results

  • Jean-Baptiste Hiriart-Urruty
  • Claude Lemaréchal
Part of the Grundlehren Text Editions book series (TEXTEDITIONS)


We start this chapter by listing some basic concepts, which are or should be wellknown — but it is good sometimes to return to basics. This gives us the opportunity of making precise the system of notation used in this book. For example, some readers may have forgotten that “i.e.” means id est, the literal translation of “that is (to say)”. If we get closer to mathematics, S∖{x} denotes the set obtained by depriving a set S function of a point x ∈ S. We also mention that, if f is a function, f −1 (y) is the inverse image of y, i.e. the set of all points x such that f(x) = y. When f is invertible, this set is the singleton {f −1(y)}.


Euclidean Space Scalar Product Orthogonal Projection Symmetric Operator Real Vector Space 
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 Berlin Heidelberg 2001

Authors and Affiliations

  • Jean-Baptiste Hiriart-Urruty
    • 1
  • Claude Lemaréchal
    • 2
  1. 1.Département de MathématiquesUniversité Paul SabatierToulouseFrance
  2. 2.INRIA, Rhône AlpesZIRSTMontbonnotFrance

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