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Math Help - Rank and rational functions

  1. #1
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    Rank and rational functions

    Suppose a matrix A (say size 6x6) has rank 2, then any diagonal element can be expressed as rational functions of certain off-diagonal elements. (Using certain 3x3 matrix determinants which are 0)

    For example
    a11 = ( a12(a41a53-a51a43) - a13(a41a52-a51a42) ) / ( a42a53-a52a43 )

    Suppose it has rank 3, can diagonal elements be expressed as rational functions of any set of off-diagonal elements (only off-diagonal) ??
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  2. #2
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    Re: Rank and rational functions

    Hey srkri.

    I'm not familiar with rational functions but wikipedia gives a ratio of two polynomials (which I'm sure is not what you are referring to), so could you please explain what a rational function is in your context?
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  3. #3
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    Re: Rank and rational functions

    I do mean rational functions as ratio of two polynomials.
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