﻿ MINVERSE function

# MINVERSE function

This article describes the formula syntax and usage of the MINVERSEfunction in Microsoft Excel.

## Description

Returns the inverse matrix for the matrix stored in an array.

## Syntax

MINVERSE(array)

The MINVERSE function syntax has the following arguments:

• Array    Required. A numeric array with an equal number of rows and columns.

## Remarks

• Array can be given as a cell range, such as A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.

• If any cells in array are empty or contain text, MINVERSE returns the #VALUE! error value.

• MINVERSE also returns the #VALUE! error value if array does not have an equal number of rows and columns.

• Formulas that return arrays must be entered as array formulas.

• Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the identity matrix — the square array in which the diagonal values equal 1, and all other values equal 0.

• As an example of how a two-row, two-column matrix is calculated, suppose that the range A1:B2 contains the letters a, b, c, and d that represent any four numbers. The following table shows the inverse of the matrix A1:B2.

 Column A Column B Row 1 d/(a*d-b*c) b/(b*c-a*d) Row 2 c/(b*c-a*d) a/(a*d-b*c)
• MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the cancellation is not complete.

• Some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a noninvertable matrix is 0.

## Example

### Example 1

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

• Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

• Press CTRL+C.

• Create a blank workbook or worksheet.

• In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.

• To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

 1 2 3 4 5
 A B Data Data 4 -1 2 0 Formula Formula =MINVERSE(A2:B3)

Notes

• The formula in the example must be entered as an array formula in the Excel desktop application. After copying the example to a blank worksheet, select the range A5:B6 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.

• In Excel Online, to view the result in its proper format, select the cell, and then on the Home tab, in the Number group, click the arrow next to Number Format, and click General.

### Example 2

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.

3. Create a blank workbook or worksheet.

4. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

 1 2 3 4 5 6
 A B C Data Data Data 1 2 1 3 4 -1 0 2 0 Formula Formula Formula =MINVERSE(A2:C4)

Notes

• The formula in the example must be entered as an array formula n the Excel desktop application. After copying the example to a blank worksheet, select the range A6:C8 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.25.

• In Excel Online, to view the result in its proper format, select the cell, and then on the Home tab, in the Number group, click the arrow next to Number Format, and click General

Tip    Use the INDEX function to access individual elements from the inverse matrix.

Applies To: Excel 2010, Excel Starter, Excel Online, SharePoint Online

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