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Excel MINVERSE Function

Excel MINVERSE function
Summary 

The Excel MINVERSE function returns the inverse matrix of a given array. The input array must contain numbers only and be a square matrix, with equal rows and columns. The result is an inverse matrix with the same dimensions as the array provided.

Purpose 
Get inverse matrix of array
Return value 
Inverse matrix of array with same dimensions
Syntax 
=MINVERSE (array)
Arguments 
  • array - A square array of numbers only.
Version 
Usage notes 

The MINVERSE function returns the inverse matrix of a given array. The product of a matrix and its inverse is the identity matrix, a n × n square matrix with ones on the main diagonal and zeros in every other position. 

The MINVERSE function takes just one argument, array, which should be a square matrix, with an equal number of rows and columns. In order for MINVERSE to calculate an inverse matrix, array must contain numbers only. When an inverse exists, MINVERSE returns an inverse matrix with the same dimensions as the array provided.

If a matrix cannot be inverted, MINVERSE will return a #NUM! error. A matrix that can't be inverted has a determinant of zero (0).

Examples

In the example shown the formula used in E7 to calculate the inverse matrix of the 2 x 2 matrix in the range B7:C8 is:

=MINVERSE(B7:C8) // returns {-2,3;3,-4}

The result is the 2 x 2 matrix seen in E7:F8, which can also be expressed as the array {-2,3;3,-4}.

The formula in M7 calculates the inverse matrix of the 3 x 3 matrix in B7:C8:

=MINVERSE(I7:K9) // returns {-24,20,-5;18,-15,4;5,-4,1}

The result is the 3 x 3 matrix seen in M7:O9, which can be expressed as the array {-24,20,-5;18,-15,4;5,-4,1}.

Array syntax

The MINVERSE function returns an array of values. In Excel 365, where dynamic arrays are native, you can use the MINVERSE function without any special handling – MINVERSE will return an array of values that spill directly into cells in the worksheet.

In versions of Excel prior to Excel 365, you need to enter MINVERSE enter as a multi-cell array formula to display results directly on the worksheet. To do this, make a selection of the right size, and enter MINVERSE with control + shift + enter.

Notes

  • The input array must be a square matrix with an equal number of rows and columns
  • The array argument can be provided as a range or array constant like {4,3;3,2}
  • Empty cells in the source array will cause MINVERSE to return the #VALUE! error
  • MINVERSE returns the #VALUE! error value if array does not have an equal number of rows and columns.
  • If a matrix cannot be inverted, MINVERSE will return a #NUM! error. 

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