MINVERSE

Microsoft Office Spreadsheet Functions

Show All

MINVERSE

See Also

Returns the inverse matrix for the matrix stored in an array.

Syntax

MINVERSE(array)

Array   is a numeric array with an equal number of rows and columns.

Remarks

  • Array can be given as a cell range, such as A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.

  • If any cells in array are empty or contain text, MINVERSE returns the #VALUE! error value.

  • MINVERSE also returns the #VALUE! error value if array does not have an equal number of rows and columns.

  • Formulas that return arrays must be entered as array formulas.
  • Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the identity matrix — the square array in which the diagonal values equal 1, and all other values equal 0.
  • As an example of how a two-row, two-column matrix is calculated, suppose that the range A1:B2 contains the letters a, b, c, and d, and that these letters represent any four numbers. The following table shows the inverse of the matrix A1:B2.
      Column A Column B
    Row 1 d/(a*d-b*c) b/(b*c-a*d)
    Row 2 c/(b*c-a*d) a/(a*d-b*c)
  • MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the cancellation is not complete.
  • Some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a noninvertable matrix is 0.

Example 1

The example may be easier to understand if you copy it to a blank spreadsheet.

How?

Data Data
4 -1
2 0
Formula Formula
=MINVERSE(A2:B3)  
   

Note   The formula in the example must be entered as an array formula. After copying the example to a blank spreadsheet, select the range A5:B6 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.

Example 2

The example may be easier to understand if you copy it to a blank spreadsheet.

How?

Data Data Data
1 2 1
3 4 -1
0 2 0
Formula Formula Formula
=MINVERSE(A2:C4)    
     
     

Note   The formula in the example must be entered as an array formula. After copying the example to a blank spreadsheet, select the range A6:C8 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.25.

Tip