Description
Multiply determinant by scale for the determinant after scaling one column.
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.
Multiply determinant by scale for the determinant after scaling one column.
When to use this tool
Use Matrix Column Scaling Determinant Factor when you need one determinant identity, sign, or small-matrix diagnostic.
How to use the tool and how it works
- Enter determinant, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read determinant. Use the output convention below.
Multiply determinant by scale for the determinant after scaling one column.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| determinant | Determinant | Required. Finite number. |
| scale | Scale | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| determinant | Determinant | Required. Finite number. |
{
"input": {
"determinant": 6,
"scale": -2
},
"output": {
"determinant": -12
}
}Limitations and assumptions
- This assumes exactly one column is scaled; no matrix is supplied to verify the operation.
- 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: Matrix Single Row Swap Determinant Sign
Validate both zero-based rows within rowCount.