Vectors and Matrices
Mathematica TE represents a vector as a list.
In[1]:= v = {a, b, c}
Out[1]= 
You can add two vectors together term by term.
In[2]:= v + {-1, 0, 1}
Out[2]= 
You can also multiply a vector by a number.
In[3]:= 10 v
Out[3]= 
This is the dot product of two vectors.
In[4]:= v . {x, y, z}
Out[4]= 
This generates a matrix whose 
element is 
. Mathematica TE represents the matrix as a list of lists.
In[5]:= m = Table[ 1 / (i + j + 1), {i, 3}, {j, 3} ]
Out[5]= 
The matrix can also be shown as a two-dimensional array.
In[6]:= MatrixForm[ % ]
Out[6]//MatrixForm= 
This is the product of the matrix m and v, treated here as a column vector.
In[7]:= m . v
Out[7]= 
Here is the inverse of the matrix.
In[8]:= Inverse[ m ]
Out[8]= 
Multiplying the inverse by the original matrix gives the 
identity matrix.
In[9]:= % . m
Out[9]= 
Mathematica TE can also manipulate symbolic matrices. This finds the eigenvectors of a matrix.
In[10]:= Eigenvectors[ {{a, b}, {-b, 2a}} ]
Out[10]= 
