A volume associated with m x n matrices

@inproceedings{BenIsrael1992AVA,
  title={A volume associated with m x n matrices},
  author={Adi Ben-Israel},
  year={1992}
}
Abstract Let Aϵ mxnr with nonzero singular values σ1, σ2,…,σr. The volume of A, vol A, is defined as zero if r = 0, and otherwise, volA = Πri=1σi, or equivalently, volA =√Σdet2AIJ, summing over all r x r nonsingularsubmatrices AIJ. The matrix volume vol A generalizes the “absolute value of the determinant” from nonsingular to arbitrary matrices. Any r-dimensional unit cube in R(AT) is mapped, under A, into a parallelepiped of volume vol A. This paper gives properties and applications of vol A… CONTINUE READING

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