Description
Check one homogeneous dot-product constraint against a supplied absolute 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.
Check one homogeneous dot-product constraint against a supplied absolute tolerance.
When to use this tool
Use Vector Nullspace Single Constraint Residual 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 row, vector, tolerance. 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 residual, satisfies. Inspect satisfies before interpreting the associated values.
Require matching row and vector dimensions and nonnegative tolerance. Return residual=dot(row,vector) and satisfies when abs(residual)<=tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Array of Finite number.; maximum items 256. |
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| tolerance | Nonnegative absolute tolerance in the quantity tested; see the stated units and boundary rule. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Finite number. |
| satisfies | Satisfies | Required. Boolean. |
{
"input": {
"row": [
1,
2
],
"vector": [
2,
-1
],
"tolerance": 0
},
"output": {
"residual": 0,
"satisfies": true
}
}Limitations and assumptions
- This checks one homogeneous linear constraint using an absolute tolerance, not an entire matrix nullspace. Empty vectors produce a zero dot product; no nontrivial solution or basis is constructed.
- 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 2d Shear Area Preservation Residual
Compare oriented planar determinants before and after a supplied x-by-y shear.
- Vector Affine Combination Weight Residual
Sum weights and return residual=sum-1.