MUNIT 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.

MUNIT returns a square identity matrix: ones on the main diagonal and zeros elsewhere. It is not a matrix of all ones. Multiplying a compatible matrix by an identity matrix leaves it unchanged in exact arithmetic. Release implementation.

MUNIT(Dimension)

• Dimension: the required size n of an n×n result. Use a positive whole number.
• The source applies its approximate-floor helper before allocating the matrix.
• INDEX(MUNIT(n);Row;Column) selects a particular one-based entry for the reproducible scalar examples.

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.

MUNIT(2) represents [[1,0],[0,1]]. Its first and fourth component examples return diagonal ones, while the two off-diagonal examples return zeros. MUNIT(1) is the one-element matrix containing 1.

For MUNIT(4), row 2 column 4 is off the diagonal and therefore zero. The native MUNIT(2.9) example selects row 2 column 2 and returns 1, consistent with the source reducing the dimension to 2. Supply an integer deliberately rather than depending on fractional-size conversion.

For any n×n matrix A, I_n×A=A×I_n=A. The determinant of I_n is 1, its inverse is itself, and its trace is n. These properties make identity matrices useful when checking an inverse or constructing a diagonal adjustment.

Adding cI_n to A changes only the diagonal entries by c; it does not add c to every cell. For example, [[1,2],[3,5]]+2I_2 is [[3,2],[3,7]]. Distinguish that operation from ordinary scalar broadcasting in a spreadsheet expression.

The source checks for a zero dimension and an implementation matrix-size limit before allocation. The native examples use sizes 1–4 and one ordinary fractional size; zero, negative, huge and near-integer rounding cases were not executed.

An identity matrix has n² entries, so choosing a very large n can be expensive even though the construction rule is simple. The checked INDEX formulas return selected components, not a saved whole-array layout or GUI spill demonstration. Matrix dimensions and placement remain separate considerations.

MMULT, MINVERSE, MDETERM.

• 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.