Description
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.
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.
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.
When to use this tool
Use Basis Vector Determinant Sign 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 basis. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sign, singular. Inspect singular before interpreting the associated values.
Require a three-by-three basis matrix. Scale each row by its largest absolute component, calculate the scaled determinant sign, and return singular for an exact zero determinant; any all-zero row immediately returns sign zero and singular true.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| basis | Basis | Required. Array of Array of Finite number.; maximum items 128.; maximum items 128. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sign | Sign | Required. Safe integer. |
| singular | Singular | Required. Boolean. |
{
"input": {
"basis": [
[
1,
0,
0
],
[
0,
1,
0
],
[
0,
0,
-1
]
]
},
"output": {
"sign": -1,
"singular": false
}
}Limitations and assumptions
- Positive row scaling preserves determinant sign and reduces overflow risk. Exact zero is a floating-point test without rank tolerance, so near-singular matrices need a separate numerical analysis.
- 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
- Vector Basis Coordinate Unit Scale
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.
- Vector Cylindrical Basis Azimuth Term
Transform vector components in the local cylindrical basis to Cartesian components at an explicit azimuth.