Abstract
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 = l 2 (n) and Y = l 2 (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.
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© 2001 Springer-Verlag New York, Inc.
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Deutsch, F. (2001). Generalized Solutions of Linear Equations. In: Best Approximation in Inner Product Spaces. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9298-9_8
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DOI: https://doi.org/10.1007/978-1-4684-9298-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2890-0
Online ISBN: 978-1-4684-9298-9
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