Linear Algebra

Saunders Mac Lane
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Saunders Mac Lane: University of Chicago, Department of Mathematics

Chapter Chapter VII in Mathematics Form and Function, 1986, pp 185-218 from Springer

Abstract: Abstract An algebraic approach to problems of plane geometry led us in §IV.7 to introduce two-dimensional vector spaces over the field R of real numbers, while in the calculus gradients and tangent lines lead to cotagent and tangent vector spaces. Three dimensional vector spaces are standard in physics, while the algebra of vectors is an effective way of handling geometrical ideas in dimensions higher than 3. Analysis soon produces infinite-dimensional spaces such as L2 (§VI.11). This chapter will summarize the properties of such linear vector spaces over an arbitrary field, not necessarily R or C.

Keywords: Vector Space; Tensor Product; Basis Vector; Linear Transformation; Linear Algebra (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-1-4612-4872-9_8

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