MDETERM 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.

MDETERM returns one number: the determinant of a square numeric matrix. It is not a sum of entries, a product of all cells or a matrix inverse. A determinant can be negative; its sign is meaningful rather than an error condition. Release implementation.

MDETERM(Array)

• Array: exactly one square numeric range or matrix expression.
• The number of rows must equal the number of columns.
• The result is scalar even when the input has many cells.

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.

Matrix A, [[1,2],[3,5]], has determinant 1*5-2*3=−1. Matrix B is triangular, so its determinant is the product of its diagonal entries, 2×3=6. The diagonal matrix D has determinant 2×4=8.

For the three-by-three Matrix C, expansion along the first row gives 1×(0−24)−2×(0−20)+3×(0−5)=1. The determinant’s calculation depends on the matrix arrangement, not just the list of nine values.

For compatible square matrices, det(A×B)=det(A)×det(B). The listed nested MMULT example gives −6, consistent with −1×6. For an invertible matrix, det(A⁻¹)=1/det(A), and the inverse-A example gives −1. The identity matrix has determinant 1.

A zero determinant indicates singularity in exact mathematics. A tiny floating-point determinant alone is not a scale-independent measure of how reliably a matrix can be inverted. Rescaling an n×n matrix by c multiplies its determinant by c^n; small determinants can therefore have different causes.

The source requires a numeric square matrix and uses pivoted LU decomposition. If its decomposition identifies singularity, MDETERM returns zero; MINVERSE has a different response because no inverse exists. Singular, nonsquare, mixed-type and oversized inputs were not executed in this ordinary fixture.

All eight examples use small valid matrices. The nested matrix expressions verify their scalar determinant path; they do not establish GUI array-entry behavior or every rounding case. Preserve row and column order when moving input data.

MINVERSE, MMULT, MUNIT.

• 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.