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

a_{11} = ( a_{12}(a_{41}a_{53}-a_{51}a_{43}) - a_{13}(a_{41}a_{52}-a_{51}a_{42}) ) / ( a_{42}a_{53}-a_{52}a_{43} )

Suppose it has rank 3, can diagonal elements be expressed as rational functions of any set of off-diagonal elements (only off-diagonal) ??

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?

Re: Rank and rational functions

I do mean rational functions as ratio of two polynomials.