MATHEMATICA TUTORIAL

# 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.
 Out[1]=
Anything that is not manifestly a list is treated as a scalar, so applying VectorQ gives False.
 Out[2]=
This is a 2×3 matrix.
 Out[3]=
For a vector, Dimensions gives a list with a single element equal to the result from Length.
 Out[4]=
This object does not count as a matrix because its rows are of different lengths.
 Out[5]=

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