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A Concise Overview of Functional Spaces in Modern Theory and Advanced Reasoning

By Rex Lucianus

A Concise Overview of Functional Spaces in Modern Theory and Advanced Reasoning Computer Science

A Concise Overview of Functional Spaces in Modern Theory and Advanced Reasoning

By Rex Lucianus

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Description
As we begin our exploration of Hilbert space, the reader is assumed to have some background in linear algebra and real analysis. Nonetheless, for the sake of clarity, we begin with a discussion of three notions that are fundamental to the field of functional analysis, namely metric spaces, normed linear spaces, and inner product spaces. Few definitions are as fundamental to analysis as that of the metric space. In essence, a metric space is simply a collection of objects (e.g. numbers, matrices, pineapple flavored Bon Bons covered with flax seeds) with an associated rule, or function, that determines "distance" between two objects in the space. Such a function is termed a metric. Perhaps the most intuitive example of a metric space is the real number line with the associated metric |x ¿ y|, for x, y ¿ R. In general, though, a metric need only satisfy four basic criteria. More formally: Deftnition (Metric Space). A metric space (X, d) is a set X together with an assigned metric function d : X × X ¿ R that has the following properties: Positive: d(x, y) ¿ 0 for all x, y, z ¿ X,
Product details
Binding:
Paperback
Number of Pages:
76
Release Date:
2025-04-25
Publication Date:
2025-04-25
Publisher:
Independent Publisher
Languages:
Original: English
ISBN13:
9798231064847
GPSR Manufacturer Reference:
[email protected]
Weight:
217 g
Height:
216 cm
Width:
280 cm
Thickness:
4 cm
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