Generalized Solutions of Linear Equations

  • Frank Deutsch
Part of the CMS Books in Mathematics / Ouvrages de mathématiques de la SMC book series (CMSBM)


In this chapter we consider the fundamental problem of solving the linear operator equation
$$ Ax = y $$
where A: XY is a bounded linear operator between the inner product spaces X and Y, and y is a given element of Y. If X = l2(n) and Y = l2(m), then (8.0.1) reduces to a system of m linear equations in n unknowns. Even in this special case, however, we know that there are three possible outcomes of (8.0.1): no solution, a unique solution, or infinitely many solutions.


Hilbert Space Linear Operator Generalize Solution Product Space Cauchy Sequence 
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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Frank Deutsch
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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