Description
Return newEntry² - oldEntry² as squaredDelta and add it to squaredNorm.
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.
Return newEntry² - oldEntry² as squaredDelta and add it to squaredNorm.
When to use this tool
Use Matrix One Entry Frobenius Norm Delta when you need one transparent matrix-update component.
How to use the tool and how it works
- Enter oldEntry, newEntry, squaredNorm. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squaredDelta, updatedSquaredNorm. Use the output convention below.
Require squaredNorm at least oldEntry². Return newEntry² - oldEntry² as squaredDelta and add it to squaredNorm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| oldEntry | Old Entry | Required. Finite number. |
| newEntry | New Entry | Required. Finite number. |
| squaredNorm | Squared Norm | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squaredDelta | Squared Delta | Required. Finite number. |
| updatedSquaredNorm | Updated Squared Norm | Required. Finite number. |
{
"input": {
"oldEntry": 3,
"newEntry": 4,
"squaredNorm": 25
},
"output": {
"squaredDelta": 7,
"updatedSquaredNorm": 32
}
}Limitations and assumptions
- The input norm must be the squared Frobenius norm before replacing this one real entry; no square root or consistency check against a full matrix is done.
- 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 Rank One Update
Add weight × leftFactor × rightFactor to entry for one entry of a rank-one update.
- Matrix Diagonal Update Trace Delta
Add increment to trace and return increment separately as delta.