Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    so..... is this right?

    An orthogonal matrix is one where when 2 of any of the columns are multiplied together they equal zero.

    eg.

    a b c
    d e f
    g h i

    is orthogonal when

    a
    d
    g

    multiplied by

    b
    e
    h

    equals zero
    Offline

    2
    ReputationRep:
    You also need that

    a
    d
    g

    multiplied by

    a
    d
    g

    equals 1, etc.

    You can put all the conditions for orthogonality together as M M^T = I.
    Offline

    10
    ReputationRep:
    A matrix is orthogonal if it's transpose equals its inverse, i.e. A^T = A^{-1}. This follows from the fact that the (dot) products of all pairs of its column vectors are zero, which in turn follows from the fact that its column vectors are normalized.

    In other words, it's not just if two columns multiplied by each other equal zero - it's:
    (a, d, g) . (b, e, h) = 0
    (a, d, g) . (c, f, i) = 0
    (b, e, h) . (c, f, i) = 0
    • Thread Starter
    Offline

    1
    ReputationRep:
    so transposing the matrix and multiplying the matrix by its transpose gets I
    • Thread Starter
    Offline

    1
    ReputationRep:
    thanks dvs - i think i get it now - at least, i get it better than i did 10 minutes ago...
 
 
 
Turn on thread page Beta
Updated: June 24, 2005
The home of Results and Clearing

3,163

people online now

1,567,000

students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
Poll
How are you feeling about GCSE results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

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