=

We can scalar multiply by
as:

For further information concerning vector spaces over finite fields,
consult my Spring 2004 report of same title.
__Vector Class__
Because a vector can be treated as a special kind of matrix, the
vector class extends the matrix class. In the next section, the
similarities between vectors and matrices will be more apparent. I
wrote the vector class with an outline similar to the one I used for
FieldElem and FPElem. The Vector class has two constructors. The
first more fundamental constructor takes an integer argument, which
sets the number of elements that given vector can hold. The second
constructor makes it possible to cast a matrix as a vector by
assuming that the argument matrix has only one column. The other
methods in this class make it possible to change one specific
element in the vector, find the number of elements in the vector,
return the value of and element at a specific location, fill the
vector with elements of zero value, and copy the vector. It is
important to fill the vector with zero valued elements so that the
vector does not contain valued elements, which can cause
later complications.
Below is a link to the java file for the Vector class.
Vector.java
__VectorOps Class__
Like with the FieldElem class, it is important to have a static
class that provides operations for the vector data type. My
VectorOps class provides a few basic methods to add, multiply, and
compare vectors. Like with FieldOps, the methods in VectorOps do not
change their arguments.
Below is a link to the java file for the VectorOps class.
VectorOps.java