Turn on thread page Beta
 You are Here: Home >< Maths

# Hermitian Matrix watch

1. I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.
2. (Original post by Benjy100)
I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.
Are you given any particular properties about U?
3. (Original post by Slowbro93)
Are you given any particular properties about U?
Sorry, I completely forgot to include that vital information, U is a unitary matrix, so U dagger = U inverse
4. (Original post by Benjy100)
I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.
Remember to use the properties of each identity:

For unitary matrices,

And in addition:

How can you use these two properties to help with your proof?

Reply
Submit reply
Turn on thread page Beta

### 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: December 26, 2014
Today on TSR

### Edexcel C4 Maths Unofficial Markscheme

Find out how you've done here

### 2,646

students online now

Exam discussions

Poll
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

### Study habits of A* students

Top tips from students who have already aced their exams

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