A homogeneous linear system can be thought as a linear transformation of a vector in dimensional space into zero vector in dimensional space.

The solution
of a homogeneous system of equations
is called the
*
null space
*
of
and the dimension of the null space is called the
*
nullity
*
of
.

The dimension of the range and the null space of a matrix are related through fundamental relationship . Where is the number of original unknowns.

**
See also
**
:
rank through RREF
,
matrix rank
,
matrix range
,
solving system linear equations

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