Description
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry.
Row margins, entry thresholds, and small-matrix criteria summarize specific algebraic conditions. They do not automatically establish a larger matrix's conditioning or spectrum.
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry.
When to use this tool
Use Matrix: Matrix Diagonal Dominance Row Margin when you need one explicitly scoped matrix bound or residual.
How to use the tool and how it works
- Enter row, diagonalIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry. Mark weaklyDominant for margin ≥ 0 and strictlyDominant for margin > 0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Array of finite number. Implementation limit: 128 items. |
| diagonalIndex | Diagonal Index | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.margin | Margin | Calculated result member: number. |
| result.weaklyDominant | Weakly Dominant | Calculated result member: boolean. |
| result.strictlyDominant | Strictly Dominant | Calculated result member: boolean. |
{
"input": {
"row": [
1,
4,
-2
],
"diagonalIndex": 1
},
"output": {
"result": {
"margin": 1,
"weaklyDominant": true,
"strictlyDominant": true
}
}
}Limitations and assumptions
- This is a one-row condition, not a proof that the whole matrix is diagonally dominant or well conditioned.
- Outputs are nested inside result. 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 the complete matrix and a suitable numerical tolerance or factorization for a global property test.
References
Similar or alternative tools
- Matrix Gershgorin One Row Disc
Select a valid diagonalIndex.
- Matrix: Matrix Entry Relative Threshold Mask
Form threshold = absoluteTolerance + relativeTolerance × referenceMagnitude, requiring all three nonnegative.