Abstract
This appendix gives a summary of the results we need from linear algebra. Recommended for further reading are Blyth and Robertson’s books Basic Linear Algebra [4] and Further Linear Algebra [5] and Halmos Finite-Dimensional Vector Spaces [11].
We expect that the reader will already know the definition of vector spaces and will have seen some examples. For most of this book, we deal with finitedimensional vector spaces over the complex numbers, so the main example to bear in mind is C n, which we think of as a set of column vectors.
We assume that the reader knows about bases, subspaces, and direct sums. We therefore begin our account by describing quotient spaces. Next we discuss the connection between linear maps and matrices, diagonalisation of matrices, and Jordan canonical form. We conclude by reviewing the bilinear algebra needed in the main text.
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© 2006 Springer-Verlag London Limited
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Erdmann, K., Wildon, M.J. (2006). Appendix A: Linear Algebra. In: Introduction to Lie Algebras. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/1-84628-490-2_16
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DOI: https://doi.org/10.1007/1-84628-490-2_16
Publisher Name: Springer, London
Print ISBN: 978-1-84628-040-5
Online ISBN: 978-1-84628-490-8
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