Free Ebook Finite-Dimensional Vector Spaces
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Book Details :
Published on: 2015-12-25
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Original language: English
Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes "My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets ...". This text is an ideal supplement to modern treatments of Linear Algebra. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --Zentralblatt für Mathematik. Vector space - Wikipedia A vector space (also called a linear space) is a collection of objects called vectors which may be added together and multiplied ("scaled") by numbers called ... Section "Dimension" subsections "Dimension" and ... Definition D Dimension. Suppose that $V$ is a vector space and $\set\vectorlistvt$ is a basis of $V$. Then the dimension of $V$ is defined by $\dimensionV=t$. Normed vector space - Wikipedia In mathematics a normed vector space is a vector space on which a norm is defined. In a vector space with 2- or 3-dimensional vectors with real-valued entries the ... Hilbert Space -- from Wolfram MathWorld A Hilbert space is a vector space H with an inner product fg such that the norm defined by f=sqrt(ff) turns H into a complete metric space. If the metric ... Euclidean space - definition of Euclidean space by The ... Noun 1. Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional metric space - a set of points ...
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