Linear Systems of Algebraic Equations

This page presents some topics from Linear Algebra needed for construction of solutions to systems of linear algebraic equations and some applications. We use matrices and vectors as essential elements in obtaining and expressing the solutions.

Numerical Methods

Numerical Methods

The condition number of an invertible matrix A is defined to be

\[ \kappa ({\bf A}) = \| {\bf A} \| \, \| {\bf A}^{-1} \| . \]

This quantity is always bigger than (or equal to) 1. We must use the same norm twice on the right-hand side of the above equation. Sometimes the notation is adjusted to make it clear which norm is being used, for example if we use the infinity norm we might write

\[ \kappa_{\infty} ({\bf A}) = \| {\bf A} \|_{\infty} \, \| {\bf A}^{-1} \|_{\infty} . \]