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.TH spaninter 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
spaninter - subspace intersection
.SH CALLING SEQUENCE
.nf
[X,dim]=spaninter(A,B [,tol])
.fi
.SH PARAMETERS
.TP 10
A, B
: two real or complex matrices with equal number of rows
.TP
X
: orthogonal or unitary square matrix
.TP
dim
: integer, dimension of subspace range(\fVA\fR) inter range(\fVB\fR)
.SH DESCRIPTION
.Vb [X,dim]=spaninter(A,B)
computes the intersection of range(\fVA\fR) and range(\fVB\fR).
.LP
The first \fVdim\fR columns of \fVX\fR span this intersection i.e.
\fVX(:,1:dim)\fR is an orthogonal basis for
.IG
range(\fVA\fR) inter range(\fVB\fR)
.FI
.LA \mbox{${\cal R}(A) \cap {\cal R}(B)$}
.LP
In the \fVX\fR basis \fVA\fR and \fVB\fR are respectively represented by:
.LP
\fVX'*A\fR and \fVX'*B\fR.
.LP
\fVtol\fR is a threshold (\fVsqrt(%eps)\fR is the default value).
.SH EXAMPLE
.nf
A=rand(5,3)*rand(3,4); // A is 5 x 4, rank=3
B=[A(:,2),rand(5,1)]*rand(2,2);
[X,dim]=spaninter(A,B);
X1=X(:,1:dim); //The intersection
svd(A),svd([X1,A]) // X1 in span(A)
svd(B),svd([B,X1]) // X1 in span(B)
.fi
.SH SEE ALSO
spanplus, spantwo
.SH AUTHOR
F. D.
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