Matrices, Norms, and Condition Numbers

Abstract

Matrix notation greatly facilitates the theoretical discussion of overdeter- mined systems, although the actual computational steps are often more effectively implemented by other means. Matrices are so familiar that to present a definition of them seems unduly formal, almost a waste of time. Nevertheless, for the sake of completeness we give a definition. A matrix is an array of mn elements, arranged in m rows and n columns

$$A = \left( {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}& \cdots &{{a_{1n}}} \\ {{a_{21}}}&{{a_{22}}}& \cdots &{{a_{2n}}} \\ \vdots & \vdots &{}& \vdots \\ {{a_{m1}}}&{{a_{m2}}}&{}&{{a_{mn}}} \end{array}} \right).$$

((2.1))

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