MINVERSE Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight ordinary scalar or INDEX-selected reference formulas were recalculated from generated ODF in 4.1.16 on Linux x86-64, Build 9816. Source and independent arithmetic were checked.

MINVERSE calculates the inverse of a square numeric matrix when the inverse exists. Its result is a matrix, not the reciprocal of each individual cell. The examples select particular result components with INDEX so that each checked formula has a scalar output. Release implementation.

MINVERSE(Array)

• Array: one square numeric range or matrix expression.
• The matrix must be nonsingular for an ordinary inverse.
• INDEX(MINVERSE(Array);Row;Column) selects a one-based result position. Matrix output dimensions match the input dimensions.

Enter these matrices as ordinary numeric cells, keeping their rows and columns in order:

The native column contains saved 4.1.16 results; independent references use high-precision arithmetic and the stated source rules. Values are shown to twelve decimal places where needed. The range examples use the numeric setup above.

For Matrix A=[[1,2],[3,5]], the inverse is [[-5,2],[3,-1]]. The first four native examples extract these four entries individually. For a two-by-two matrix [[a,b],[c,d]], the inverse is [[d,-b],[-c,a]]/(a*d-b*c) when the denominator is nonzero.

The diagonal Matrix D=[[2,0],[0,4]] has diagonal inverse entries 0.5 and 0.25. This special diagonal case permits reciprocal diagonal values; it does not justify taking cell-by-cell reciprocals for a general matrix.

Check an inverse by multiplying it with the original matrix and inspecting the residual against the identity matrix. For A, the exact multiplication gives [[1,0],[0,1]]. Individual floating-point residuals may be tiny rather than exactly zero.

Matrix C has determinant 1 and inverse [[−24,18,5],[20,−15,−4],[−5,4,1]]. The examples explicitly check its top-left and bottom-right entries. A full residual calculation is more informative than checking just one large or small inverse entry.

The source uses LU decomposition and solves for each inverse column. It checks numeric, square dimensions and rejects a decomposition it identifies as singular. Those invalid or ill-conditioned cases were not part of the native fixture, and the small examples do not certify stability for arbitrary matrices.

All checked formulas extract scalar entries through INDEX. No whole-matrix spill, selection-size or GUI array-entry behavior is claimed. If the task is solving a linear system rather than displaying an inverse, consider the numerical method separately instead of assuming explicit inversion is always the most stable approach.

MDETERM, MMULT, INDEX.

• Function-specific release implementation

The generated ODF produced the informational load warning “Not all attributes could be read.” The sheet was hard-recalculated and saved separately. All eight ordinary formula identities, inputs and selected results were reconciled; a stale SUM cache changed from 999999 to 3 and an uncached SUM returned 7. This establishes the stated examples, not every workbook style, invalid input or GUI whole-array entry. INDEX wrappers select individual returned components. Other explanatory identities are independent calculations. The authoring-tool XLSX was not executed in OpenOffice, and its preview values are not the native results reported here.