Vectors and Matrices

You can use lists to generate matrices and vectors. We can think of
list as a vector or a row of a matrix. A list of lists is then a two
dimension array of objects, like a m x n matrix. 

In order to represent a two component vector you type in,

	In[1]:= {x,y}

	Out[1]= {x, y}

To represent a 2 x 2 matrix,

	In[2]:= {{1,2},{3,4}} //MatrixForm
	                    1  2
                     
	Out[2]//MatrixForm= 3  4

The //MatrixForm displays the list in a matrix form.

You can also perform vector and matrix operations. For example, a
scalar or dot product of vectors or multiplication of two matrices.

	In[3]:= v = {x,y}

	Out[3]= {x, y}

	In[4]:= v . v
	         2    2
	Out[4]= x  + y

	In[5]:= A = {{1,2},{3,4}}

	Out[5]= {x, y}

	In[7]:= A . A

	Out[7]= {{7, 10}, {15, 22}}	

The following are some standard functions used for vectors in
Mathematica.

	Table[f,{i,n}]	builds a vector of length 'n' by evaluating
			'f' with i=1, i=2,..., i=n.
	Array[a,n]	builds a vector of length 'n' of the form
			{a[1],a[2],....}
	Range[n]	create a list {1,2,3,...,n}
	list[[i]]	gives the ith element in list
	Length[list]	gives the length of the list
	//Columnform	displays the list in column form

Similar commands which are applicable to matrices are given below.

	Table[f,{i,m},{j,n}]	builds a m x n matrix, evaluating 'f'
				with 'i' and 'j' ranging from 1 to m
				and 1 to n respectively.	
	Array[a,{m,n}]		builds an m x n matrix with elements
				a[i,j] with 'i' ranging from 1 to m
				and 'j' ranging from 1 to n.
	IdentityMatrix[n]	generates a n x n identity matrix.
	DiagonalMatrix[list]	creates a diagonal matrix with
				elements of the list along its
				diagonal. 
	list[[i]]		gives the ith row of the matrix.
	list[[i,j]]		gives the i,jth element of the matrix.
	Dimensions[list]	gives the dimension of a matrix
				represented by the list.
	MatrixForm[list]	displays the list in a matrix form.