matrix problem
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From: dushya on 20 Mar 2010 02:47 A is a matrix. B is its inverse. elements of A (and hence B) depend diffentiably on some parameter s. the problem is to prove -- B(i,j)dA(j,i)/ds = (1/det(A)) d(det(A))/ds where repeated indices on LHS are summed. det(A) means determinant of A. waiting for reply (with solution) thanks
From: Robert Israel on 21 Mar 2010 15:11
dushya <sehrawat.dushyant(a)gmail.com> writes: > A is a matrix. B is its inverse. elements of A (and hence B) depend > diffentiably on some parameter s. the problem is to prove -- > B(i,j)dA(j,i)/ds = (1/det(A)) d(det(A))/ds > where repeated indices on LHS are summed. det(A) means determinant of > A. > > waiting for reply (with solution) > thanks Hint: you may find Cramer's Rule useful, in the form B = adj(A)/det(A). -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |