Quadratic Forms rank and signature confusion











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I would just like to clear some things up!
A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?



Many thanks!






quadratic-forms matrix-rank







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    up vote
    0
    down vote

    favorite












    I would just like to clear some things up!
    A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
    Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?



    Many thanks!






    quadratic-forms matrix-rank







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I would just like to clear some things up!
      A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
      Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?



      Many thanks!






      quadratic-forms matrix-rank







      share|cite|improve this question













      I would just like to clear some things up!
      A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
      Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?



      Many thanks!






      quadratic-forms matrix-rank




      quadratic-forms matrix-rank






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 2 days ago









      MathematicianP

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