# Matrix computation over modulo N

**URL:** <https://community.wolfram.com/t/matrix-computation-over-modulo-n/18326>\
**Category:** Questions\
**Tags:** algebra\
**Created:** [June 23, 2021, 8:59am UTC](https://community.wolfram.com/t/matrix-computation-over-modulo-n/18326 "2021-06-23T08:59:18Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![gpai5095](https://avatars.discourse-cdn.com/v4/letter/g/f1d935/32.png) [@gpai5095](https://community.wolfram.com/u/gpai5095)\
**Post date:** [June 23, 2021, 8:59am UTC](https://community.wolfram.com/t/matrix-computation-over-modulo-n/18326/1 "2021-06-23T08:59:18Z")

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Hi,

I am just starting with Mathematica. Is there an easy way to do matrix computations over the field Zn (1,2,…,n-1)? For example, I would like to find the eigensystem of a matrix M over Z5 or the reduced echelon form of a matrix over Z5. I know the functions Eigensystem[] and RowReduce[] but is there any way to add an argument so that I can obtain the results over the field Z5?

Thanks in advance

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<div class="post-metadata">

**Author:** ![danl](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/danl/32/41267_2.png) [@danl](https://community.wolfram.com/u/danl)\
**Post date:** [June 23, 2021, 2:05pm UTC](https://community.wolfram.com/t/matrix-computation-over-modulo-n/18326/2 "2021-06-23T14:05:41Z")

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The documentation for `RowReduce` indicates quite clearly how to provide a modulus. `Eigensystem` does not accept a modulus; it is not obvious how to represent those eigenvalues that lie in an extension field of Z/\<5\>.