MINVERSE in Excel

Article byJeevan A Y
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

MINVERSE Function in Excel

The MINVERSE function in Excel stands for “Matrix Inverse.” This built-in Excel function converts the given matrix to the inverse matrix with the same number of arrays.

Having talked about the “inverse matrix,” one needs to understand the “inverse matrix.”

Inverse Matrix: The reciprocal of a number is called the “inverse matrix.” For example, for the number 5, we can write the reciprocal as:

So, we can write the inverse matrix in the same logic using this equation “A-1.” We can write the above number as 5-1 as well. When we multiply a number by its reciprocal we always get 1. For example, if the number 5 is multiplied by its reciprocal 1/5, we get the result of 13.

Inverse Matrix 1

Similarly, when we multiply a matrix by its inverse, we get the identity matrix, “I.” Below is the equation of the identity matrix.

A * A-1 = I

When discussing the inverse matrix in excelInverse Matrix In ExcelAn inverse matrix is defined as the reciprocal of a square matrix that is a non-singular matrix. The inverse matrix in excel has an equal number of rows and columns to the original matrix.read more we must look at the identity matrix. With an identity matrix, all the rows and columnsRows And ColumnsA cell is the intersection of rows and columns. Rows and columns make the software that is called excel. The area of excel worksheet is divided into rows and columns and at any point in time, if we want to refer a particular location of this area, we need to refer a cell.read more are in equal numbers. So diagonally, we get 1 as the value; apart from diagonal, everything else will equal zero.

So, the identity matrix will always be “2 * 2, 3 * 3, 4 * 4” like this.

Once the matrix is inverted, we can cross-check whether it is inverted using MMULT functionMMULT FunctionThe MMULT function in Excel is an inbuilt function for matrix multiplication. It accepts two arrays as arguments and returns the product of the two arrays. read more in Excel. We will get an identity matrix that looks like this.

Inverse Matrix 1-1

Let us try these things with Excel now.

Minverse-in-Excel

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Example of using MINVERSE Excel Function

You can download this MINVERSE in Excel Template here – MINVERSE in Excel Template

For example, take a look at the below 3 * 3 matrix.

inverse matrix in Excel - Example 2
  • We have matrix numbers from A2 to C4. To reverse this matrix, create an identical table next to the above table but do not keep the same values and keep the field empty.
inverse matrix in Excel - Example 2-1
  • In the range E2 to G4, we will create an inverse of the matrix. First, select the range of cells from E2 to G4.
Minverse in Excel - Example 2-2
  • Now, in the selected range of cells, open the Excel MINVERSE function.
Minverse in Excel - Example 2-3
  • The first argument of the MINVERSE function is an array. It is the range of matrix values that we are trying to inverse, so our 3 * 3 matrix values are in the range of A2 to C4.
Minverse in Excel - Example 2-4

Before closing the formula, we need to remember that “MINVERSE” is an array, so we need to close out the formula using the “CSE” keys.

Note: CSE stands for “Ctrl + Shift + Enter”. So, all the array formulas are closed with these keys only.

  • So, close the formula by pressing the “ENTER” key by holding the “Ctrl + Shift” key together.
Minverse in Excel - Example 2-5

As we can see above, we have an “inverse matrix” using the MINVERSE function. Since it is an array formula, we can see curly brackets ({}) at the start and end of the array formula.

We can cross-check whether this matrix is inversed or not by using the MMULT function. MMULT function stands for “Matrix Multiplication.”

  • Now, select the range of cells to create another identity matrix, so choose the 3 * 3 matrix area.
Minverse in Excel - Example 2-6
  • Now, open the MMULT function for the selected range of cells.
Minverse in Excel - Example 2-7
  • For the array1 argument of MMULT function, choose “Matrix 1” range from A2 to C4.
Example 2-8
  • For the array2 argument of the MMULT function, choose the “inverse matrix” range of cells from E2 to G4.
Example 2-9
  • The MMULT is also an array function, so close the formula by using the “CSE” keys to convert it to an array function.
Example 2-10
  • This result has given us decimal results, so use the ROUND function inside the array function to get an accurate “identity matrix.”
Example 2-11

Now, we have an “identity matrix” with 1 as the diagonal value. Like this, we can use the MINVERSE function to inverse the matrix and MMULT to check whether it is reversed or not.

Things to Remember

This article is a guide to MINVERSE in Excel. We learn how to use the MINVERSE function to inverse the matrix and the ROUND and MMULT formula to get the identity matrix, along with an example and downloadable Excel template. You may learn more about Excel from the following articles: –