how to construct an orthogonal matrix
in [Matlab]
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From: yuan on 9 Mar 2010 22:24 Hi everybody, I'm stuck with a simple problem about how to construct an orthogonal matrix R, say of size m * n. Note that here m<n, for example, m = 20, n =100. I try both SVD and Gram–Schmidt process, but i fail because the result is a special matrix in which (n-m) columns are zero. Can anyone help me? Thanks a lot:)
From: Matt J on 9 Mar 2010 23:00 "yuan " <tianyuan_2003(a)163.com> wrote in message <hn73cn$aqp$1(a)fred.mathworks.com>... > Hi everybody, > > I'm stuck with a simple problem about how to construct an orthogonal matrix R, say of size m * n. Note that here m<n, for example, m = 20, n =100. > > I try both SVD and Gram–Schmidt process, but i fail because the result is a special matrix in which (n-m) columns are zero. =============== What makes this a failure?
From: TideMan on 9 Mar 2010 23:19 On Mar 10, 4:24 pm, "yuan " <tianyuan_2...(a)163.com> wrote: > Hi everybody, > > I'm stuck with a simple problem about how to construct an orthogonal matrix R, say of size m * n. Note that here m<n, for example, m = 20, n =100. > > I try both SVD and Gram–Schmidt process, but i fail because the result is a special matrix in which (n-m) columns are zero. > > Can anyone help me? > > Thanks a lot:) R=randn(m,n); perhaps??
From: yuan on 9 Mar 2010 23:54 thank you for the suggestion. The following is my code: a = rand(20,100); c=mgrscho(a); // the Gram-sch process however c'*c =/= I (identity matrix)
From: Walter Roberson on 10 Mar 2010 00:09
yuan wrote: > > thank you for the suggestion. > The following is my code: > > a = rand(20,100); > c=mgrscho(a); // the Gram-sch process > > however c'*c =/= I (identity matrix) M = [eye(5), zeros(5,4)]; c = M'; c' * c ans = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 |