Sign in to follow this  

Do you know this matrix?

This topic is 4488 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hi All, Here's a matrix with elements A-I:
M =[
A B C
D E F
G H I
]
So, a bit of a long shot here, but does anyone then recognise the following symmetrical 4x4 matrix:
N = [
A+E+I F-H   G-C    B-D
F-H   A-E-I B+D    G+C
G-C   B+D   -A+E-I F+H
B-D   G+C   F+H    -A-E+I
]
( BTW the sum of its diagonal elements is zero. ) Any hints at all would be gratefully received. Thanks in advance, Graham [Edited by - Fruny on August 30, 2005 10:08:29 AM]

Share this post


Link to post
Share on other sites
A context would help a great deal. It looks familar, but without a context I can't even guess where I saw it at. One observation is that zero maps to zero, but nothing maps to identity.

Share this post


Link to post
Share on other sites
My apologies, I should have given more context. It's from Berthold Horn's paper on absolute orientation (See Page 7 of http://people.csail.mit.edu/bkph/papers/Absolute_Orientation.pdf) Although I have made full practical use of this paper, I'd like to, but can't follow its derivation of matrix N.

I'm hoping someone may recognise the pattern of elements in N, perhaps from another area of mathematics where I may get a second chance to understand it.

Share this post


Link to post
Share on other sites
I'm afraid it was just a vague similarity to other things rather than a vague memory of this particular matrix. The basic layout of the matrix is similar to a matrix representation of a quaternion. The main diagonal is similar to the components of the product of two quaternions. My knowledge of quaternions is extremely limited. My only experience with them is as a type of number in abstract algebra. We did a section on relating quaternions represented as 4x4 matrices to 3x3 orthonormal matrices, but I can't find the notes.

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
I briefly looked over the paper you linked. It appears that N is derived in the section immediately preceding the one where M and N are written out. N is first derived as a summation of matrix products.

The section describing M and N apparently constructs M as another way to explain the matrix N and how it works, but it doesn't seem that N is directly derived from M, rather it is a different way of viewing the matrix.

Share this post


Link to post
Share on other sites

This topic is 4488 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this