## 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.

 VectorQ[expr] give True if expr has the form of a vector, and False otherwise MatrixQ[expr] give True if expr has the form of a matrix, and False otherwise Dimensions[expr] a list of the dimensions of a vector or matrix

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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