# Rank of matrix on Z2 field

**URL:** <https://discourse.julialang.org/t/rank-of-matrix-on-z2-field/81078>\
**Category:** New to Julia\
**Tags:** math, matrices, fast-math\
**Created:** [May 14, 2022, 11:52pm UTC](https://discourse.julialang.org/t/rank-of-matrix-on-z2-field/81078 "2022-05-14T23:52:53Z")\
**Posts on this page:** 1\
**Showing post:** 9

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**Author:** ![jd-foster](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jd-foster/32/35824_2.png) [@jd-foster](https://discourse.julialang.org/u/jd-foster)\
**Post date:** [May 15, 2022, 10:20am UTC](https://discourse.julialang.org/t/rank-of-matrix-on-z2-field/81078/9 "2022-05-15T10:20:38Z")

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There was a previous discussion and example given here:

> [@Rank is wrong for Rational matrices](https://discourse.julialang.org/t/rank-is-wrong-for-rational-matrices/19380):
>
> consider the matrix: julia\> m=[1//(n+m) for n in 1:11, m in 1:11]; it can be inverted exactly with no problem: julia\> one(m)==inv(m)\*m true however: julia\> rank(m) 10 The reason is that rank begins by converting its argument to floating-point. It seems to me that given a field (Rationals, but it could be rational fractions or any other field), the rank should be computed by computing the echelon form of the matrix rather that trying to convert to floats (which would not make sense for r…

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