Description
Select a valid diagonalIndex.
Row margins, entry thresholds, and small-matrix criteria summarize specific algebraic conditions. They do not automatically establish a larger matrix's conditioning or spectrum.
Select a valid diagonalIndex.
When to use this tool
Use Matrix Gershgorin One Row Disc 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 center, radius. Use the output convention below.
Select a valid diagonalIndex. Return that row entry as center and the sum of absolute other entries as radius.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Array of finite number; maximum items 256. |
| diagonalIndex | Diagonal Index | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| center | Center | Required. Finite number. |
| radius | Radius | Required. Finite number. |
json
{
"input": {
"row": [
2,
-3,
4
],
"diagonalIndex": 0
},
"output": {
"center": 2,
"radius": 7
}
}Limitations and assumptions
- This constructs one real-centered Gershgorin disc; it does not compute eigenvalues or verify the remaining matrix rows.
- 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: Matrix Diagonal Dominance Row Margin
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry.
- Matrix: Matrix Entry Relative Threshold Mask
Form threshold = absoluteTolerance + relativeTolerance × referenceMagnitude, requiring all three nonnegative.