MINVERSE

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

• The size of the array must not exceed 52 columns by 52 rows. If it does, the function returns a #VALUE! error.
• 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 that 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 worksheet.

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
1. Press CTRL+C.
2. In the worksheet, select cell A1, and press CTRL+V.
3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.
A B
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 worksheet, 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 worksheet.

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
1. Press CTRL+C.
2. In the worksheet, select cell A1, and press CTRL+V.
3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.
A B C
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 worksheet, 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    Use the INDEX function to access individual elements from the inverse matrix.

Applies to:
Excel 2003