2x2 Cofactor Calculator
Actual2×2signedcofactor(−1)^(row+column)timesminor,zero-basedindices0/1,finitebinary64.
Description
A cofactor combines a deletion minor with a row-and-column sign.
A cofactor combines a deletion minor with a row-and-column sign.1
This tool returns the signed cofactor of a 2-by-2 matrix using zero-based indices.
When to use 2x2 Cofactor Calculator
Use this tool to obtain the signed cofactor of a 2-by-2 matrix using zero-based indices.
How to use 2x2 Cofactor Calculator and how it works
- Prepare actualMatrix, actualRowIndex, actualColumnIndex, with the units, conventions and assumptions below.
- Enter the required fields and run 2x2 Cofactor Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualMatrix | Exactly two rows of two finite entries, using the row and column ordering below. | array of array of number | Required; other constraints below |
| actualRowIndex | Zero-based row index, integer 0 or 1. | number | Required; integer 0–1; finite; other constraints below |
| actualColumnIndex | Zero-based column index, integer 0 or 1. | number | Required; integer 0–1; finite; other constraints below |
Require a finite 2-by-2 matrix and zero-based integer row and column indices, each 0 or 1. Select the opposite entry and apply the parity sign (-1)^(row+column). Return that signed cofactor, without transposing it as an adjugate entry.
cofactor(row,column)=(-1)^(row+column)*A[1-row][1-column] Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualMatrix": [
[
1,
2
],
[
3,
4
]
],
"actualRowIndex": 0,
"actualColumnIndex": 1
},
"output": {
"result": {
"value": -3
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use 2x2 Eigenvectors Calculator for a complementary operation: A real matrix can have real, repeated or complex eigenvalues, and repeated values do not ensure diagonalizability.
Use 2x2 Condition Number Calculator for a complementary operation: A spectral condition number compares the largest and smallest singular values of a matrix.
References
-
2x2 Cofactor Calculator — tool.io
Similar or alternative tools
- 2x2 Eigenvectors Calculator
A real matrix can have real, repeated or complex eigenvalues, and repeated values do not ensure diagonalizability.
- 2x2 Condition Number Calculator
A spectral condition number compares the largest and smallest singular values of a matrix.