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Matrix Groups

Produktform: E-Buch Text Elektronisches Buch in proprietärem

These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphic. In Chapter I "group" is defined and examples are given; ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A ~ 0 , and define the general linear group GL(n,k) We construct the skew-field lli of to operate linearly on llin quaternions and note that for A E Mn(lli) we must operate on the right (since we mUltiply a vector by a scalar n on the left). So we use row vectors for R , en, llin and write xA for the row vector obtained by matrix multiplication. We get a ~omplex-valued determinant function on Mn (11) such that det A ~ 0 guarantees that A has an inverse.weiterlesen

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Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-1-4612-5286-3 / 978-1461252863 / 9781461252863

Verlag: Springer US

Erscheinungsdatum: 06.12.2012

Seiten: 228

Auflage: 2

Autor(en): M. L. Curtis

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