MAGMA Computational Algebra System

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 x n matrix A, return m, the number of rows of A.

NumberOfColumns(A) : Mtrx -> RngIntElt

Ncols(A) : Mtrx -> RngIntElt

Given an m x 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.