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.
- 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.
Remarks
- 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.
Examples
MINVERSE({4,-1;2,0}) equals {0,0.5;-1,2}
MINVERSE({1,2,1;3,4,-1;0,2,0}) equals {0.25,0.25,-0.75;0,0,0.5;0.75,-0.25, -0.25}
Tip Use the INDEX function to access individual elements from the inverse matrix.