This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 3.7.3 Scalars, Vectors and Matrices Mathematica represents matrices and vectors using lists. Anything that is not a list Mathematica considers as a scalar. A vector in Mathematica consists of a list of scalars. A matrix consists of a list of vectors, representing each of its rows. In order to be a valid matrix, all the rows must be the same length, so that the elements of the matrix effectively form a rectangular array. Functions for testing the structure of vectors and matrices. The list {a,b,c} has the form of a vector. In[1]:= VectorQ[ {a, b, c} ] Out[1]= Anything that is not manifestly a list is treated as a scalar, so applying VectorQ gives False. In[2]:= VectorQ[ x + y ] Out[2]= This is a matrix. In[3]:= Dimensions[ {{a, b, c}, {ap, bp, cp}} ] Out[3]= For a vector, Dimensions gives a list with a single element equal to the result from Length. In[4]:= Dimensions[ {a, b, c} ] Out[4]= This object does not count as a matrix because its rows are of different lengths. In[5]:= MatrixQ[ {{a, b, c}, {ap, bp}} ] Out[5]=