# What is the significance of the matrix inversion

## MINV (function)

The MINVERSE function returns the inverse matrix for a matrix stored in an array.

Note: If you have an up-to-date version of Microsoft 365, you can just type the formula in the top left cell of the output range and then the ENTER Press to confirm the formula as a dynamic array formula. Otherwise, the formula must be entered as a conventional array formula by first selecting the output range, entering the formula in the cell in the top left of the output range, and then using CTRL + SHIFT + ENTER is confirmed. Excel automatically inserts curly braces at the beginning and end of the formula. For more information about array formulas, see Array Formula Guidelines and Examples.

### syntax

MINV (matrix)

The MINV function syntax has the following arguments:

• matrix Required. A square matrix (the number of rows and columns is identical)

### Hints

• Matrix can be specified as a cell range, for example as A1: C3, as a matrix constant, for example {1.2.3; 4.5.6; 7.8.9}, or as a name for one of these two possibilities.

• If cells in a matrix are empty or contain text, MINVERSE returns a #VALUE! displayed.

• MINVERSE also gives a #VALUE! error if matrix does not have the same number of rows and columns.

• Inverse matrices, like determinants in general, are used to solve systems of equations with several variables. The product of a matrix and its inverse is the identity matrix, a square matrix in which the elements on the main diagonal are 1 and all other elements are 0.

• As an example of calculating a matrix of two rows and two columns, assume that the range A1: B2 contains the letters a, b, c, and d, which represent any four numbers. The following table shows the inverse of the matrix A1: B2.

Column A.

Column B

line 1

d / (a ​​* d-b * c)

b / (b * c-a * d)

line 2

c / (b * c-a * d)

a / (a ​​* d-b * c)

• MINV is calculated with an accuracy of approximately 16 digits. This can lead to a small numerical error if not properly rounded.

• Some square matrices cannot be inverted and give the #NUM! error value with MINVERSE. The determinant for an irreversible matrix is ​​0.

### Examples  You must enter the above formulas as array formulas in order for them to work properly. After entering the formula, press the Enter if you have a current Microsoft 365 subscription. Press otherwise, CTRL + SHIFT + ENTER. If the formula is not entered as an array formula, a single result is returned.

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