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.
