{"product_id":"matrix-groups-9780387960746","title":"Matrix Groups","description":"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.\u003cbr\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":50323984646418,"sku":"9780387960746","price":84.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_af2a95c8-f23e-4325-85dd-8f9a00142410.jpg?v=1727663417","url":"https:\/\/surprise-castle.myshopify.com\/products\/matrix-groups-9780387960746","provider":"Surprise Castle","version":"1.0","type":"link"}