Turn on thread page Beta
    • Thread Starter

    Could someone please help me with this question:

    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!

    What have you done so far? What are your thoughts?
    • Thread Starter

    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...
Submit reply
Turn on thread page Beta
Updated: February 8, 2010
Favourite type of bread
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.