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]= |  |
| 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]= |  |
