# Elementary Properties

The following functions yield elementary properties of matrices and may be applied to matrices of any type, including vectors.

## `NumberOfRows(A): Mtrx -> RngIntElt`

## `Nrows(A): Mtrx -> RngIntElt`

Given an $m \times n$ matrix $A$, return $m$, the number of rows of $A$.

## `NumberOfColumns(A): Mtrx -> RngIntElt`

## `Ncols(A): Mtrx -> RngIntElt`

Given an $m \times n$ matrix $A$, return $n$, the number of columns of $A$.

## `NumberOfNonZeroEntries(A): Mtrx -> RngIntElt`

## `NNZEntries(A): Mtrx -> RngIntElt`

Given a matrix $A$, return the number of non-zero entries in $A$.

## `Density(A): Mtrx -> FldRe`

Given a matrix $A$, return the density of $A$ as a real number, which is the number of non-zero entries in $A$ divided by the product of the number of rows of $A$ and the number of columns of $A$ (or zero if $A$ has zero rows or columns).

## `BaseRing(A): Mtrx -> Rng`

## `CoefficientRing(A): Mtrx -> Rng`

Given a matrix $A$ with entries lying in a ring $R$, return $R$.

## `ElementToSequence(A): Mtrx -> [ RngElt ]`

## `Eltseq(A): Mtrx -> [ RngElt ]`

Given a matrix $A$ over the ring $R$ having $m$ rows and $n$ columns, return the entries of $A$, in row-major order, as a sequence of $mn$ elements of $R$.

## `RowSequence(A): Mtrx -> [ [RngElt] ]`

Returns the entries of $A$ as a sequence of rows where a row is represented as a sequence of entries of $A$.