Abstract
In this chapter we review certain basic concepts from linear algebra. Although our treatment is self-contained, the reader is assumed to be familiar with the basic operations on matrices. After reviewing basic matrix operations and definitions, we recall concepts such as Schur complement, inverse of a partitioned matrix and Cauchy–Binet formula. Important properties of eigenvalues of symmetric matrices, including Spectral Theorem and Interlacing Theorem are reviewed. Basic notions of generalized inverses, including Moore–Penrose inverse are stated. Relevant concepts and results are given, although we omit the proofs.
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Bapat, R.B.: Linear Algebra and Linear Models, 2nd edn. Hindustan Book Agency, New Delhi, and Springer, Heidelberg (2000)
Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)
Bondy, J.A., Murty, U.S.R.: Graph Theory, Graduate Texts in Mathematics, 244. Springer, New York (2008)
Campbell, S.L., Meyer, C.D.: Generalized Inverses of Linear Transformation. Pitman, London (1979)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)
West, D.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, New Delhi (2002)
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© 2014 Springer-Verlag London
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Bapat, R.B. (2014). Preliminaries. In: Graphs and Matrices. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-6569-9_1
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DOI: https://doi.org/10.1007/978-1-4471-6569-9_1
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