1. ## Simple Question about fields

So we've just learned about fields and there are some questions in our assignment, and I need some clarification:

ex. What is the rank of A (a matrix given) over the fields Q, F4, etc etc

what does it mean when it asks "over the field"? I can find the rank easily, but the field part is confusing me

any help is appreciated!

2. Originally Posted by dr4g0n9
So we've just learned about fields and there are some questions in our assignment, and I need some clarification:

ex. What is the rank of A (a matrix given) over the fields Q, F4, etc etc

what does it mean when it asks "over the field"? I can find the rank easily, but the field part is confusing me

any help is appreciated!
it means that the entries of your matrix come from that field. for example consider the matrices $A=\begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}, \ \ B=\begin{pmatrix}0 & 1 \\ 1 & 1 \end{pmatrix}.$

if we consider these matrices over $\mathbb{R}$ we get: $A+B=\begin{pmatrix}1 & 3 \\ 1 & 2 \end{pmatrix}$ and if we consider them over $\mathbb{F}_3$ we'll have $A+B=\begin{pmatrix}1 & 0 \\ 1 & 2 \end{pmatrix}.$