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By Kardi Teknomo, PhD.
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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.
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See also: rank through RREF, matrix rank, matrix range, solving system linear equations
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Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
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