Description
Calculate one ordered antisymmetric bivector coordinate from two supplied vectors.
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 one ordered antisymmetric bivector coordinate from two supplied vectors.
When to use this tool
Use Vector Bivector Single Coordinate 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 first, second, i, j. 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 coordinate. Use the output convention below.
Require aligned first and second vectors and distinct valid zero-based i and j. Return coordinate=first[i]*second[j]-first[j]*second[i].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Array of Finite number.; maximum items 256. |
| second | Second | Required. Array of Finite number.; maximum items 256. |
| i | I | Required. Safe integer; minimum 0. |
| j | J | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
{
"input": {
"first": [
1,
2,
3
],
"second": [
4,
5,
6
],
"i": 0,
"j": 2
},
"output": {
"coordinate": -6
}
}Limitations and assumptions
- Swapping coordinate order reverses its sign. This is one antisymmetric bivector coordinate, not the complete wedge product, a normalized area, or a three-dimensional cross product in arbitrary dimensions.
- 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 3d Coordinate Cyclic Permutation
Cyclically reorder three coordinates by an integer shift modulo three.
- Vector Basis Coordinate Unit Scale
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.