Abstract
Let V be a vector space over the field C of complex numbers and let GL(V) be the group of isomorphisms of V onto itself. An element a of GL(V) is, by definition, a linear mapping of V into V which has an inverse a-1; this inverse is linear. When V has a finite basis (e i ) of n elements, each linear map a: V → V is defined by a square matrix (a ij ) of order n. The coefficients a ij are complex numbers; they are obtained by expressing the images a(e j ) in terms of the basis (e i ):
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© 1977 Springer-Verlag, New York Inc.
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Serre, JP. (1977). Generalities on linear representations. In: Linear Representations of Finite Groups. Graduate Texts in Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9458-7_1
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DOI: https://doi.org/10.1007/978-1-4684-9458-7_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9460-0
Online ISBN: 978-1-4684-9458-7
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