Generalized Solutions of Linear Equations
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
where A: X → Y 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.
$$ Ax = y $$
KeywordsHilbert Space Linear Operator Generalize Solution Product Space Cauchy Sequence
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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© Springer-Verlag New York, Inc. 2001