You are Here: Home >< Maths

# Rank in Linear Maps watch

Let S: U -> V, T:V->W be linear maps, where U, V, W are vector spaces over the same field K.
Prove (i) Rank(TS) <= Rank (S)
(ii) If V=W and T is non singular, then Rank(TS) = Rank(S)

Thank you!
2. What have you done so far? What are your thoughts?
3. sorry firstly I just realised that I posted a smiley where it's suppose to be a U.

I'm thinking Rank(TS) is T: U -> W so it's less than or equal to dim(U) by the dimension theorem, and maybe incorporate somehow the fact that Rank(S) is also less than or equal to dim(U)...
As for part 2, I honestly dont even know where to begin...

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 8, 2010
Today on TSR

### Summer Bucket List is Back!

Start yours and you could win £150!

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams