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Aide Scilab >> Algèbre Lineaire > Subspaces > spanplus


sum of subspaces

Calling Sequence



A, B

two real or complex matrices with equal number of rows


orthogonal or unitary square matrix

dim, dima

integers, dimension of subspaces


nonnegative real number


computes a basis X such that:

the first dima columns of X span Range(A) and the following (dim-dima) columns make a basis of A+B relative to A.

The dim first columns of X make a basis for A+B.

One has the following canonical form for [A,B]:

[*,*]    (dima rows)
X'*[A,B]=[0,*]    (dim-dima rows)

tol is an optional argument (see function code).


A=rand(6,2)*rand(2,5);      // rank(A)=2
B=[A(:,1),rand(6,2)]*rand(3,3);   //two additional independent vectors

See Also

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Last updated:
Tue Apr 02 17:36:45 CEST 2013