An orthogonal matrix from two orthognal matrices!

Dear All.. I have two orthogonal matrices, A and B, where

A is (256 by 256) elements, A*A'=I; and B is (256 by 256) elements, B*B'=I.

Let C is a matrix formed by a combination of A and B such that:

C is (256 by 256) and C(1:128,:)=A(1:128,:); C(129:256,:)=B(1:128,:);

Unfortunately, C is not orthogonal, i.e. C*C~=I; so, how can i do some changes on C to make it orthogonal, let's say C1 is the orthogonal matrix extracted from C. I need C1 to be in the closest form (such as mesh plots) to C?

is there any method for that? looking forward to get your help best regards sam..

Answer 1

[Jan]

The question is not clear. Your matrix C is not guaranteed to have full rank. Then a procedure to "make it orthonormal" is not straight. I do not understand the description "closest form as mesh plots".

[wissam]

hi jan,

thanks for the reply..

I just have a matrix C and wanna make it an orthogonal one.. any procedure that i can use such as SVD decomposition to extract an orthogonal matrix from C?

okay, you ignore what i have said.. "closest form as mesh plots"..

best regards..

Answer 2

[G A]

will this help?

doc orth

[wissam]

hi GA,

thanks for your reply..

when i try to use: b=orth(C), this gives me a matrix b and its orthogonal but when i do mesh plot it, the plot is like random numbers not similar to C shape that what i want.. i want ot generate b is similar (in the closet plot)to C but orthogonal..

thanks..

Answer 3

[Bjorn Gustavsson]

It doesn't necessarily work that way that the matrix (with vectors) spanning the same space as the columns of your matrix C is similar to C in a spatial sense. You might be able to resort the columns of C1 to make it looking nicer (at least different). But this is the way it is. You might have to learn to look at the new base-vectors of C1 one by one (or a few at a time).