Property	Value
Hex Value	`$0C`
Categories	Operators
Localizations	FR: `⁻¹`

`⁻¹`

Overview

Availability: Token available everywhere.

Syntax

⁻¹

Description

The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.

The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.

4ֿ¹
        .25
{1,2,3}ֿ¹
        {1 .5 .3333333333}
[[3,2][4,3]]ֿ¹
        [[3  -2]
         [-4 3 ]]

Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.

Optimization

Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:

:(P+√(P²-4Q))/2
can be
:2ֿ¹(P+√(P²-4Q

This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:

7fPart(4292/7
        1
7fPart(7ֿ¹4292
        .9999999999

Error Conditions

ERR:DIVIDE BY 0 is thrown when trying to take the reciprocal of 0.
ERR:SINGULAR MAT is thrown when trying to invert a singular matrix.

²
³

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

History

Calculator	OS Version	Description
TI-82	1.0	Added

Authors: Adrien Bertrand

⁻¹