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  • Users: rainwyz0706
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  1. R

    Second and third isomorphism theorem

    I've recently encountered some forms of the second and third isomorphism theorem, but I don't quite get them. Could anyone explain in a bit of details please? I guess my thought was not in the right direction or something. (Second isomorphism theorem) Let A be a subring and I an ideal of the...
  2. R

    Spectral theorem for self-adjoint linear transformations

    Let P,Q be self-adjoint linear transformations from V to V, Q is also positive-definite. Deduce that there exist scalars λ1 , . . . , λn and linearly independent vectors e1 , . . . , en in V such that, for i, j = 1, 2, . . . , n: (i) P ei = λi Qei ; (ii) <P ei , ej > = δi j λi ; (iii) <Qei ...