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.
References and Further Reading
- [Bap00]Bapat, R.B.: Linear Algebra and Linear Models, 2nd edn. Hindustan Book Agency, New Delhi, and Springer, Heidelberg (2000)Google Scholar
- [BG03]Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Google Scholar
- [BM08]Bondy, J.A., Murty, U.S.R.: Graph Theory, Graduate Texts in Mathematics, 244. Springer, New York (2008)Google Scholar
- [CM79]Campbell, S.L., Meyer, C.D.: Generalized Inverses of Linear Transformation. Pitman, London (1979)Google Scholar
- [HJ85]Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)Google Scholar
- [Wes02]West, D.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, New Delhi (2002)Google Scholar