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NullSpace
NullSpace[
m
] gives a list of vectors that forms a basis for the null space of the matrix m.
NullSpace works on both numerical and symbolic matrices.
NullSpace[
m
,
Modulus->
n
] finds null spaces for integer matrices modulo n.
NullSpace[
m
,
ZeroTest
->
test
] evaluates test
[
m
[[
i
,
j
]]
] to determine whether matrix elements are zero. The default setting is ZeroTest
->
Automatic.
A Method option can also be given. Possible settings are as for LinearSolve.
See the Mathematica book: Section 3.7.8.
See also: LinearSolve, RowReduce, SingularValues.
Further Examples
The nullspace of a non-singular matrix is the trivial vector space. In other words, no nonzero vector gets multiplied to the zero vector.
In[1]:= 
Out[1]= 
This nullspace has dimension  .
In[2]:= 
Out[2]= 
We check the result.
In[3]:= 
Out[3]= 
This set of vectors spans the nullspace of the  x  matrix.
In[4]:= 
Out[4]= 
Multiplying any linear combination of these vectors by the matrix gives the zero vector.
In[5]:= 
Out[5]= 
We simplify by expanding.
In[6]:= 
Out[6]= 
The rank of the matrix is the difference between the number of columns and the dimension of the nullspace.
In[7]:= 
Out[7]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
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