15.1.11 Kernel of a linear function
The ker
or kernel
or nullspace
command finds a basis for the kernel of a linear function.
-
ker takes
A, a matrix representing a linear function with respect to the
standard basis.
- ker(A) returns a list of vectors that is a basis of
the kernel of the linear function.
- The Nullspace
command is the inert form of nullspace.
Example
| ker([[1,1,2],[2,1,3],[3,1,4]]) |
Remark.
The Nullspace command is only useful in Maple mode.
(See Section 2.5.2; you can get into Maple mode by
hitting the state line red button then Prog style, then
choosing Maple and clicking Apply.)
-
Nullspace takes
A, an integer matrix representing a linear function with respect
to the standard basis.
- Nullspace(A) mod p returns a list of
vectors that is a basis for the kernel of the linear transformation
ℤ/pℤ[X].
Examples
| Nullspace([[1,1,2],[2,1,3],[3,1,4]]) |
Input in Maple mode:
| Nullspace([[1,2],[3,1]]) mod 5 |
In Xcas mode, the equivalent input is:
| nullspace([[1,2],[3,1]] % 5) |