A to Z of Excel Functions: The MINVERSE Function
13 June 2022
Welcome back to our regular A to Z of Excel Functions blog. Today we look at the MINVERSE function.
The MINVERSE function
![](http://sumproduct-4634.kxcdn.com/img/containers/main/blog-pictures/2022/a-to-z/296/image1.jpeg/d11ea51cbcf71f50d6c96dab7152d119.jpg)
In mathematics, especially in areas such as linear algebra, matrices may be used to solve simultaneous equations. For the record, a matrix is not just a movie it’s a rectangular arrangement of m x n elements, in the dimensions of m rows by n columns, e.g. a matrix A (say) may be represented as
![](http://sumproduct-4634.kxcdn.com/img/containers/main/blog-pictures/2022/a-to-z/296/image2.png/f32e5a15e2cf9c3e4d2d058458ce054d.jpg)
It is often written in compact form as
![](http://sumproduct-4634.kxcdn.com/img/containers/main/blog-pictures/2022/a-to-z/296/image3.png/f1140ff857fc3b6f5f97a6a24f4a6fc7.jpg)
An n x n square matrix A is called invertible (also non-singular or non-degenerate), if there exists an n x n square matrix B such that
AB = BA =In
where In denotes the n x n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A?1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is zero. Singular matrices are rare in the sense that if a square matrix's entries are randomly selected from any finite region on the number line or complex plane, the probability that the matrix is singular is zero [0], that is, it will "almost never" be singular. Non-square matrices (m x n matrices for which m ? n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m x n and the rank of A is equal to n (n ? m), then A has a left inverse, an n x m matrix B such that BA = In. If A has rank m (m ? n), then it has a right inverse, an n x m matrix B such that AB = Im.
The Excel function MINVERSE returns the inverse matrix for a matrix stored in an array. It has the following syntax:
MINVERSE(array)
where:
- array is required, and represents a numerical array with an equal number of rows and columns.
It should be noted that:
- array may be given as:
- a cell range, e.g. A1:C3
- an array constant, such as {1,2,3;4,5,6;7,8,9}
- a name to either of these
- MINVERSE returns the #VALUE! error when:
- any cells in array are empty or contain text
- array does not have an equal number of rows and columns
- matrix determinants are generally used for solving systems of mathematical equations that involve several variables
- MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete. For example, the determinant of a singular matrix may differ from zero by 1E-16
- some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a non-invertible matrix is zero [0].
If you have a current version of Microsoft 365, then you can simply enter the formula in the top-left-cell of the output range, then press ENTER to confirm the formula as a dynamic array formula. Otherwise, the formula must be entered as a legacy array formula by first selecting the output range, entering the formula in the top-left-cell of the output range, and then pressing CTRL + SHIFT + ENTER to confirm it. Excel inserts curly brackets (“braces”) at the beginning and end of the formula.
As an example:
![](http://sumproduct-4634.kxcdn.com/img/containers/main/blog-pictures/2022/a-to-z/296/image4.png/72aa864d2854c6fefb1083fba0ab5792.jpg)
We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.
A full page of the function articles can be found here.