Cat::Matrix

Category of matrices

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

Cat::Matrix(R)

Description

Cat::Matrix(R) represents the category of matrices over the rng R.

A Cat::Matrix(R) is a matrix of arbitrary dimension over a component ring R.

In the following description of the methods, we use the following notations for a matrix A from a domain of category Cat::Matrix(R):

nrows(A) denotes the number of rows and ncols(A) the number of columns of A.

Further on, a row index is an integer ranges from 1 to nrows(A), and a column index is an integer ranges from 1 to ncols(A).

Parameters

R

A domain which must be from the category Cat::Rng (a ring without unit).

Entries

"coeffRing"

is set to R.

Methods

expand all

Basic Methods

new — Matrix definition

new(m, n)

Of course, this method may implement further possibilites to create matrices (for example, see the method "new" of the domain constructor Dom::Matrix).

Mathematical Methods

_plus — Add matrices

_plus(A1, A2, …)

The matrices must be of the same domain type, otherwise FAIL is returned.

identity — Identity matrix

identity(n)

It only exists if R is of category Cat::Ring, i.e., a ring with unit.

iszero — Test on zero matrices

iszero(A)

Note that there may be more than one representation of the zero matrix of a given dimension if R does not have the axiom Ax::canonicalRep.

Access Methods

concatMatrix — Horizontal concatenation of matrices

concatMatrix(A, B)

An error message is issued if the two matrices do not have the same number of rows.

delCol — Deleting columns

delCol(A, c)

If A only consists of one column then NIL is returned.

delRow — Deleting rows

delRow(A, r)

If A only consists of one row then NIL is returned.

setRow — Replacing rows

setRow(A, r, v)

stackMatrix — Appending of matrices vertically

stackMatrix(A, B)

An error message is issued if the two matrices do not have the same number of columns.

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