A Short Excursion into Matrix Algebra

  • Wolfgang Karl HärdleEmail author
  • Léopold Simar


This chapter serves as a reminder of basic concepts of matrix algebra, which are particularly useful in multivariate analysis. It also introduces the notations used in this book for vectors and matrices. Eigenvalues and eigenvectors play an important role in multivariate techniques. In Sect. 2.2 and 2.3, we present the spectral decomposition of matrices and consider the maximization (minimization) of quadratic forms given some constraints.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ladislaus von Bortkiewicz Chair of StatisticsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institute of Statistics, Biostatistics and Actuarial SciencesUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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