If 
is a linear
transformation of 
,
then the null space Null(
),
also called the kernel 
, is the set of all vectors 
such that
 |
i.e.,
 |
The term "null space" is most commonly written as two separate words (e.g., Golub and Van Loan 1989, pp. 49 and 602; Zwillinger 1995, p. 128), although other authors write it as a single word "nullspace" (e.g., Anton 1994, p. 259; Robbin 1995, pp. 123 and 180).
Each null space vector corresponds to a zero eigenvector of the transformation matrix of 
.
The Wolfram Language command NullSpace[
v1, v2, ...
] returns a list of vectors forming a vector
basis for the nullspace of a set of vectors 
over the rationals (or more generally, over whatever
base field contains the input vectors).
