How to compute tr(M^-1) ?

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#612

From: Hidetoshi SHIMODAIRA
Date: Sun, 11 Oct 1992 13:14

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I have a question as how to compute trace of inverse of matrix M.

M is a real matrix, (not suppose symmetry), and eigen values within
zero to unity, that is, a1 >= a2 >=  an.
Some of ai's are zero, so I want to compute

tr(M^-) = 1/a1 + 1/a2 + ... + 1/ak,
where a1,...,ak are not zero and a_(k+1),...,an are zero.

Is there any elegant method to compute this?



 //\\\
  @ @     Hidetoshi SHIMODAIRA    <shimo@bcl.t.u-tokyo.ac.jp>
   O      Dept. of Math. Eng. & Info. Physics, Univ. of Tokyo

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From: shimo@bcl.t.u-tokyo.ac.jp (Hidetoshi SHIMODAIRA)
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Subject: How to compute tr(M^-1) ?
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Date: 11 Oct 92 13:14:04 GMT
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