Verwandte Artikel zu Matrix Groups (Universitext)

Matrix Groups (Universitext) - Softcover

Buch 135 von 261: Universitext

Curtis, M. L.

 
9780387960746: Matrix Groups (Universitext)
Softcover
ISBN 10: 0387960740 ISBN 13: 9780387960746
Verlag: Springer, 2013

Inhaltsangabe

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.

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These notes were developed from a course taught at Rice University 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 some students to some of the concepts of Lie group theory --all done at the concrete level of matrix groups.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
0387960740
ISBN 13 
9780387960746
Einband
Taschenbuch
Auflage
2
Anzahl der Seiten
242
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