Property	Value
Hex Value	`$B4`
Categories	Catalog > I Matrix > Math
Localizations	FR: `identité(`

`identity(`

Overview

Returns the identity matrix of dimension rows x dimension columns.

Availability: Token available everywhere.

Syntax

identity(dimension)

Arguments

Name	Type	Optional
dimension

Location

2nd, matrix, MATH, 5:identity(

Description

The identity( command generates an identity matrix: that is, a matrix [B] such that for any other matrix [A], [A]*[B]=[A] (if [A] is the right size to make the multiplication valid).

The identity matrix is square (that is, the row dimension equals the column dimension); all of its elements are 0 except for the elements along the main diagonal (the diagonal going from top left to bottom right).

The command itself takes one argument: the size of the matrix, used for both row and column size, that is, identity(n) creates an n by n matrix.

:dim([A]
:identity(Ans(2→[B]
:[A][B]=[A]  // should always return 1, meaning 'true'

Optimization

The identity( command can be used as a quick way to create an empty square matrix: 0identity(n) will create an n by n matrix containing only 0 as an element. This is faster and smaller than the dim( and Fill( commands used for the same purpose:

:{5,5→dim([A]
:Fill(0,[A]
can be
:0identity(5→[A]

Error Conditions

ERR:INVALID DIM occurs if the size is not an integer 1-99. In practice, however, identity(21) is already too large for the calculator to generate.
ERR:MEMORY occurs if the size of the created matrix exceeds memory limits. This limit is hard-fixed to 3611 bytes (the size of a 20x20 matrix), regardless of having sufficient RAM to hold a larger matrix.

det(

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

History

Calculator	OS Version	Description
TI-82	1.0	`identity` added
TI-83	0.01013	Renamed `identity` to `identity(`

Authors: Adrien Bertrand

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