# Get and Sign a Note on the Volume Form in Normal Matrix Space Docentes Professor Ufabc Edu

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Differential of the function mk 1 form with respect to the variables wk wk dk 1 dmk mk dw1 dw2 dwd wk w2 wd 1 wd the partial derivatives in Eqs. F Proof The main ingredient is Sard s theorem 7. Consider the map M i j zi zj zi z j where zi are the eigenvalues of M. Thus the differential vector operator can be written as t z1 zn w12 w n 1 n z1 zn w12 w n 1 n where and z z The Jacobian matrix of the coordinate change can then be written as matrix product Jac M Now realizing the explicit...
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