Numerical Operations on Matrices

Jean-Pierre Corriou
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Jean-Pierre Corriou: University of Lorraine

Chapter Chapter 4 in Numerical Methods and Optimization, 2021, pp 107-148 from Springer

Abstract: Abstract Numerical calculation makes an extensive use of matrices. Many general properties about matrices and their properties are first detailed. Linear transformations, eigenvalues properties, and use with Gershgorin and Cayley–Hamilton theorems, the power method are explained. Similar matrices, Hermitian matrices, matrix norms, condition number are detailed. Finally, Rutishauser’s, Householder’s, Francis’s reduction methods are examined. All these methods are accompanied by complete numerical examples.

Date: 2021
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DOI: 10.1007/978-3-030-89366-8_4

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