Description
Require nonzero rowScale and columnScale and return entry × columnScale / rowScale.
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.
Require nonzero rowScale and columnScale and return entry × columnScale / rowScale.
When to use this tool
Use Matrix Diagonal Similarity One Entry Factor when you need one transparent matrix-update component.
How to use the tool and how it works
- Enter entry, rowScale, columnScale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read entry. Use the output convention below.
Require nonzero rowScale and columnScale and return entry × columnScale / rowScale.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entry | Entry | Required. Finite number. |
| rowScale | Row Scale | Required. Finite number. |
| columnScale | Column Scale | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| entry | Entry | Required. Finite number. |
{
"input": {
"entry": 6,
"rowScale": 2,
"columnScale": 3
},
"output": {
"entry": 9
}
}Limitations and assumptions
- This is one entry of D^-1 A D using the corresponding diagonal scales, not a congruence transformation or conditioning assessment.
- 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 Diagonal Congruence Entry Factor
Multiply rowFactor and columnFactor for factor and multiply both with entry for transformedEntry.
- Matrix One Entry Rank One Update
Add weight × leftFactor × rightFactor to entry for one entry of a rank-one update.