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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} ]


Anything that is not manifestly a list is treated as a scalar, so applying VectorQ gives False.

In[2]:= VectorQ[ x + y ]


This is a matrix.

In[3]:= Dimensions[ {{a, b, c}, {ap, bp, cp}} ]


For a vector, Dimensions gives a list with a single element equal to the result from Length.

In[4]:= Dimensions[ {a, b, c} ]


This object does not count as a matrix because its rows are of different lengths.

In[5]:= MatrixQ[ {{a, b, c}, {ap, bp}} ]