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student::isFree -- test for linear independence of vectors

Introduction

student::isFree(S) tests if the vectors given in S are linear independend.

Call(s)

student::isFree(S)

Parameters

S - set or list of vectors (of category Cat::Matrix) defined over a Cat::Field)

Returns

either TRUE or FALSE.

Related Functions

linalg::basis

Details

Example 1

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]

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