Description
Validate both zero-based rows within rowCount.
A determinant encodes signed volume scaling and changes predictably under elementary row or column operations. Small-matrix identities depend on entry order and exact algebraic assumptions.
Validate both zero-based rows within rowCount.
When to use this tool
Use Matrix: Matrix Single Row Swap Determinant Sign when you need one determinant identity, sign, or small-matrix diagnostic.
How to use the tool and how it works
- Enter firstRow, secondRow, rowCount. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Validate both zero-based rows within rowCount. Return determinantMultiplier -1 for distinct rows and 1 for an identical-row no-op, with changed accordingly.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstRow | First Row | Required. Safe integer. |
| secondRow | Second Row | Required. Safe integer. |
| rowCount | Row Count | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.determinantMultiplier | Determinant Multiplier | Calculated result member: number. |
| result.changed | Changed | Calculated result member: boolean. |
{
"input": {
"firstRow": 0,
"secondRow": 1,
"rowCount": 3
},
"output": {
"result": {
"determinantMultiplier": -1,
"changed": true
}
}
}Limitations and assumptions
- This models one row-swap effect without calculating a determinant or mutating a matrix.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a stable factorization for full determinants and a scale-aware numerical analysis for near-singular matrices.
References
Similar or alternative tools
- Matrix Column Swap Parity Factor
Return factor one when left and right column indices agree, otherwise minus one.
- Matrix Column Scaling Determinant Factor
Multiply determinant by scale for the determinant after scaling one column.