MINVERSE Function (Gnumeric)
Find and verify Gnumeric matrix inverses with MINVERSE, solve a small linear system and distinguish singularity, shape errors and numerical sensitivity.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: For the 2-by-2 matrix with rows 4,7 and 2,6, MINVERSE has the mathematical result 0.6,-0.7;-0.2,0.4. Multiplication by the original matrix checks that this is an inverse.
Availability and evidence
- Introduction: Gnumeric 0.32: NEWS explicitly says MDETERM and MINVERSE were implemented.
- Source support: Registered in the Gnumeric 1.12.62 plugin. No retirement is established. The last functioning application version is unverified for this guide.
- Evidence dates: Official 1.12.62 source was retained October 13–14, 2026 and reviewed October 15. Exact string and rational-matrix reference checks are independent calculations, not native Gnumeric, headless application or GUI execution.
Exact syntax and domain
=MINVERSE(matrix)
The required matrix must be square and nonempty. The pinned callback returns #VALUE! for a nonsquare or empty shape. It returns #NUM! when the inversion routine reports failure, including the documented noninvertible case. An inverse is a matrix B for which AB and BA are identity matrices; it is not a matrix of entrywise reciprocals.
The result has the same dimensions as the input. Gnumeric’s pinned manual documents selecting the complete output range, entering an array formula and confirming with Ctrl+Shift+Enter. Use that procedure for the multi-cell results below; automatic spill behavior and current GUI rendering were not exercised.
Reproducible inverse worksheet
Create InverseCheck. Put the following numeric matrix in A2:B3:
| Row | A | B |
|---|---|---|
| 2 | 4 | 7 |
| 3 | 2 | 6 |
Select D2:E3 and enter =MINVERSE(A2:B3) as an array formula. The exact mathematical reference is:
| Row | D | E |
|---|---|---|
| 2 | 0.6 | -0.7 |
| 3 | -0.2 | 0.4 |
For a 2-by-2 matrix with entries a,b;c,d, the inverse is 1/(ad-bc) times d,-b;-c,a. Here the determinant is 46-72=10, giving the stated fractions. This arithmetic independently establishes the expected coefficients; it does not certify the last displayed floating-point digit in an application.
Select G2:H3 and enter =MMULT(A2:B3,D2:E3). The reference result is 1,0;0,1. Repeat the product in the opposite order in another 2-by-2 region. Both products should be close to the identity, allowing ordinary numerical residuals rather than requiring exact text equality of displayed decimals.
Reference matrices and failure controls
| Control | Independent reference result |
|---|---|
[4,7;2,6] |
[0.6,-0.7; -0.2,0.4] |
Identity2 |
[1,0; 0,1] |
[2,0;0,4] |
[0.5,0; 0,0.25] |
[2,0,0;0,3,0;0,0,4] |
[0.5,0,0; 0,1/3,0; 0,0,0.25] |
[1,2;2,4] singular |
#NUM! |
2-by-3 nonsquare |
#VALUE! |
These bracketed matrices show rows separated by semicolons for explanation; enter their elements into cells rather than copying that notation as an unverified localized array literal. The singular control has its second row exactly twice its first. There is no unique inverse even though each individual cell contains a valid number.
Advanced: solve a two-equation system
Keep the original coefficient matrix and enter numeric 1 in J2 and 0 in J3. Select L2:L3 and enter =MMULT(D2:E3,J2:J3) as an array formula. The reference solution is x=0.6, y=-0.2.
Substitution verifies it independently: 40.6+7(-0.2)=1 and 20.6+6(-0.2)=0. The right-hand side is a two-row, one-column vector, so the solution is also a two-row, one-column vector. A transposed row vector would not have the required inner dimension.
In a copy change J3 to 1. The solution becomes -0.1,0.2, satisfying 4*(-0.1)+70.2=1 and 2(-0.1)+6*0.2=1. This changed-input test checks the entire workflow rather than only the original inverse table.
Advanced: distinguish invertibility from stability
Consider a separate coefficient matrix 1,1;1,1.0001. Its exact determinant is 0.0001, and its mathematical inverse is 10001,-10000;-10000,10000. A small determinant alone is not a complete condition estimate, but these large opposing coefficients make cancellation and sensitivity visible in this example.
With right-hand side 2,2.0001, the reference solution is 1,1. Changing only the second value to 2.0002 changes the solution to 0,2. The input change is 0.0001, yet both solution components move by one. Inverting successfully does not establish that rounded or noisy input data supports a stable interpretation.
Keep full stored precision and inspect residuals A*x-b. Rounded display values are useful for reading but should not replace the coefficients in subsequent formulas. The exact sensitivity example is a rational-arithmetic control; no native conditioning threshold or numerical error bound is claimed.
Errors, typing and troubleshooting
The shared matrix reader propagates error cells. It converts physically empty cells to zero and Boolean values to one or zero through the numeric helper. A blank in a coefficient range can therefore change the matrix or make it singular instead of acting as a missing-value marker.
Text is passed to a numeric conversion helper; malformed strings and locale-dependent numeric text are not certified here. Use actual numeric coefficients, with row and column labels outside the range. If #VALUE! appears, count rows and columns. If #NUM! appears, check for dependent rows, duplicate rows or a zero row, while remembering that backend numerical failure can require further investigation.
Do not replace a failed inverse with zero or an identity matrix merely to suppress an error. That substitutes a different mathematical model. Large matrices, nearly singular native thresholds, overflow, GUI entry and export behavior remain unverified; the source contract and the exact small reference calculations are the evidence for this guide.