# 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]= | |