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Math Help - invertible to positive absolute link

  1. #1
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    invertible to positive absolute link

    why if a matrices is not invertible then its not absolute positive
    ?
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  2. #2
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    Re: invertible to positive absolute link

    positive-definite matrices cannot be singular. suppose so, then for a positive-definite matrix A, there is some x ≠ 0, with Ax = 0. hence x^T(Ax) = 0, contradicting the fact that A is positive-definite.

    since a positive-definite matrix is non-singular, it posseses an inverse, so any non-invertible matrix cannot possibly be positive-definite.
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  3. #3
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    Re: invertible to positive absolute link

    yes i understand now
    if its definite positive then all of its eigenvalues are positive
    T(v)=kv the only way for T(v)=0 is that v=0
    so the kerT={0}
    so its invertible
    but our A is not invertible so its not definite positive
    correct?

    thanks
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  4. #4
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    Re: invertible to positive absolute link

    that is a valid argument also.
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