Description
Add increment to trace and return increment separately as delta.
A local matrix update changes a single entry or algebraic component under stated assumptions. Trace, squared norm, and Schur terms each respond to different structures.
Add increment to trace and return increment separately as delta.
When to use this tool
Use Matrix Diagonal Update Trace Delta when you need one transparent matrix-update component.
How to use the tool and how it works
- Enter trace, increment. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read updatedTrace, delta. Use the output convention below.
Add increment to trace and return increment separately as delta.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| trace | Trace | Required. Finite number. |
| increment | Increment | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| updatedTrace | Updated Trace | Required. Finite number. |
| delta | Delta | Required. Finite number. |
json
{
"input": {
"trace": 10,
"increment": 3
},
"output": {
"updatedTrace": 13,
"delta": 3
}
}Limitations and assumptions
- This assumes exactly one diagonal entry changes by increment; off-diagonal updates do not affect trace.
- 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 a full matrix operation when validating shape, factor correspondence, pivot choices, or global numerical properties.
References
Similar or alternative tools
- Matrix One Entry Frobenius Norm Delta
Return newEntry² - oldEntry² as squaredDelta and add it to squaredNorm.
- Matrix One Entry Rank One Update
Add weight × leftFactor × rightFactor to entry for one entry of a rank-one update.