student::isFree
-- test for
linear independence of vectorsstudent::isFree
(S
) tests if the vectors
given in S
are linear independend.
student::isFree(S)
S |
- | set or list of vectors (of category Cat::Matrix ) defined over a Cat::Field ) |
student::isFree
(S
) gives
TRUE
if S
is free, i.e. the vectors of
S
are linear independend. Otherwise the value
FALSE
is returned.We define 3 vectors:
>> x := matrix( [[2,3,4]] ): y := matrix( [[1,-1,1]] ): z := matrix( [[2,3,5]] ):
And we ask if x, y and z are linear independend.
>> student::isFree( {x,y,z} )
TRUE
Hence, the vectors x,y,z are linear independent, and therefore the set x,y,z is a basis of R^3 Of course the vectors x,y and (x-y) are not linear independent:
>> student::isFree( [x,y,x-y] )
FALSE
If we have vectors from different vector spaces,
student::isFree
will give an error message:
>> zz := matrix( [[2,3,5,6]] ): student::isFree( {x,y,zz} )
Error: set contains incompatible vectors [student::isFree]