Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica >
Mathematica Tutorial
|Functions »

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]:=
Click for copyable input
Out[1]=
Anything that is not manifestly a list is treated as a scalar, so applying VectorQ gives False.
In[2]:=
Click for copyable input
Out[2]=
This is a 2×3 matrix.
In[3]:=
Click for copyable input
Out[3]=
For a vector, Dimensions gives a list with a single element equal to the result from Length.
In[4]:=
Click for copyable input
Out[4]=
This object does not count as a matrix because its rows are of different lengths.
In[5]:=
Click for copyable input
Out[5]=
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team