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.TH spanplus 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
spanplus - sum of subspaces
.SH CALLING SEQUENCE
.nf
[X,dim,dima]=spanplus(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, dima
: integers, dimension of subspaces
.TP
tol
: nonnegative real number
.SH DESCRIPTION
.Vb [X,dim,dima]=spanplus(A,B)
computes a basis X such that:
.LP
the first \fVdima\fR columns of \fVX\fR span Range(\fVA\fR)
and the following (\fVdim-dima\fR) columns make a basis of \fVA+B\fR
relative to \fVA\fR.
.LP
The \fVdim\fR first columns of \fVX\fR make a basis for \fVA+B\fR.
.LP
One has the following canonical form for \fV[A,B]\fR:
.nf
[*,*] (dima rows)
X'*[A,B]=[0,*] (dim-dima rows)
[0,0]
.fi
.LP
\fVtol\fR is an optional argument (see function code).
.SH EXAMPLE
.nf
A=rand(6,2)*rand(2,5); // rank(A)=2
B=[A(:,1),rand(6,2)]*rand(3,3); //two additional independent vectors
[X,dim,dimA]=spanplus(A,B);
dimA
dim
.fi
.SH SEE ALSO
spaninter, im_inv, spantwo
.SH AUTHOR
F. D.
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