Hi,(adsbygoogle = window.adsbygoogle || []).push({});

We recently started analyzing linear machines using matrix algebra. Unfortunately, I haven't had much exposure to operating in finite fields aside from the extreme basics (i.e. the definitions of GF(P)). I can get matrix multiplication/addition, etc. just fine, but it's when finding the properties of a matrix that I'm confused.

How do we know if the rows of a matrix over GF(p) are linearly independent?

More specifically, how can I tell if two nonidentical matrices have the same row space, or if the row space of matrix A is a subspace of the row space of matrix B?

I suspect the answer to my first question is just to do Gaussian elimination and look at the rank instead of doing any algebraic manipulation such as (c1*row1 + c2*row2... ) and so forth.

But suppose I've got two matrices in row echelon form. How would I compare the rowspans of both matrices once I've done that?

I may be missing something very obvious, so your patience is appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Matrix algebra over finite fields

**Physics Forums | Science Articles, Homework Help, Discussion**