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Unitarization of complex symmetric matrices

G J N Brown and D S F Crothers

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Given any complex symmetric non-singular (n*n) matrix S we show that it is always possible to find a (2n-1)*(2n-1) matrix X which is complex symmetric and unitary, and which contains S as its leading minor. We also prove that, of the set of all complex symmetric unitary matrices which contain S as their leading minor, X is the smallest such matrix. We apply this result to the scattering matrix of atomic collision theory to correct a loss of unitarity due to the use of a finite basis set in the solution of a collision problem.


PACS

02.10.Yn Matrix theory

34.50.-s Scattering of atoms and molecules

MSC

15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)

47A40 Scattering theory (See also 34L25, 35P25, 81Uxx)

Subjects

Atomic and molecular physics

Mathematical physics

Dates

Issue 8 (21 April 1994)



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