Description
Return minor multiplied by (-1)^(row + column), using nonnegative zero-based indices.
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.
Return minor multiplied by (-1)^(row + column), using nonnegative zero-based indices.
When to use this tool
Use Matrix Determinant Single Entry Sensitivity when you need one determinant identity, sign, or small-matrix diagnostic.
How to use the tool and how it works
- Enter minor, row, column. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return minor multiplied by (-1)^(row + column), using nonnegative zero-based indices.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| minor | Minor | Required. Finite number. |
| row | Row | Required. Safe integer; minimum 0. |
| column | Column | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"minor": 3,
"row": 1,
"column": 2
},
"output": {
"derivative": -3
}
}Limitations and assumptions
- This is determinant sensitivity to one entry when minor is its corresponding deleted-row/column determinant; the minor is supplied rather than computed.
- 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: Matrix Single Entry Cofactor Sign
Return +1 when row + column is even and -1 when odd, using zero-based indices.
- Principal Two By Two Minor
Compute a × d - b × c for the supplied two-by-two minor.