MATRIX SCALING WITH RESPECT TO THE MAXIMUM-NORM, THE SUM-NORM, AND THE EUCLIDEAN NORM,
Interim technical rept.,
TEXAS UNIV AUSTIN COMPUTATION CENTER
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The condition number of a nonsingular matrix A with respect to the inversion problem and with respect to a vector norm is defined by condA lubAlubA superscript-1, where lub. denotes the matrix bound subordinate to the norm. The spectral condition number can be regarded as a measure by which A fails to be a scalar multiple of a unitary matrix. Other such measures are considered and related to condA.
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