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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