Description
Calculate determinant=aa*bb-ab² from supplied nonnegative aa and bb and nonnegative tolerance.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Calculate determinant=aa*bb-ab² from supplied nonnegative aa and bb and nonnegative tolerance.
When to use this tool
Use Vector Gram Determinant Roundoff Check when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter aa, bb, ab, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read determinant, nonnegativeWithinTolerance. Inspect nonnegativeWithinTolerance before interpreting the associated values.
Calculate determinant=aa*bb-ab² from supplied nonnegative aa and bb and nonnegative tolerance. Return nonnegativeWithinTolerance when determinant>=-tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| aa | Aa | Required. Finite number; minimum 0. |
| bb | Bb | Required. Finite number; minimum 0. |
| ab | Ab | Required. Finite number. |
| tolerance | Absolute tolerance in determinant units; determinant is not clamped. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| determinant | Determinant | Required. Finite number. |
| nonnegativeWithinTolerance | Nonnegative Within Tolerance | Required. Boolean. |
{
"input": {
"aa": 4,
"bb": 9,
"ab": 3,
"tolerance": 0
},
"output": {
"determinant": 27,
"nonnegativeWithinTolerance": true
}
}Limitations and assumptions
- A small negative determinant is reported unchanged, not clamped. The tool does not derive inner products from vectors or verify a whole Gram matrix; tolerance is in determinant units.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Basis Vector Determinant Sign
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.
- Vector Rejection Norm Roundoff Gap
Subtract squaredProjection from squaredNorm for raw.