Description
Return firstX × secondY - firstY × secondX as signedDeterminant and its magnitude as absoluteArea.
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 firstX × secondY - firstY × secondX as signedDeterminant and its magnitude as absoluteArea.
When to use this tool
Use Two Row Area Determinant when you need one determinant identity, sign, or small-matrix diagnostic.
How to use the tool and how it works
- Enter firstX, firstY, secondX, secondY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedDeterminant, absoluteArea. Use the output convention below.
Return firstX × secondY - firstY × secondX as signedDeterminant and its magnitude as absoluteArea.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstX | First X | Required. Finite number. |
| firstY | First Y | Required. Finite number. |
| secondX | Second X | Required. Finite number. |
| secondY | Second Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedDeterminant | Signed Determinant | Required. Finite number. |
| absoluteArea | Absolute Area | Required. Finite number. |
{
"input": {
"firstX": 2,
"firstY": 1,
"secondX": 1,
"secondY": 3
},
"output": {
"signedDeterminant": 5,
"absoluteArea": 5
}
}Limitations and assumptions
- The area is that of the parallelogram spanned by the two vectors, not a triangle; orientation depends on coordinate order.
- 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
- Principal Two By Two Minor
Compute a × d - b × c for the supplied two-by-two minor.
- Matrix Determinant Single Entry Sensitivity
Return minor multiplied by (-1)^(row + column), using nonnegative zero-based indices.