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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]= 
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