Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Virtual Book > Mathematics and Algorithms > Linear Algebra > Scalars, Vectors, and Matrices >
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 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
Format:   HTML  |  CDF