Description
Multiply rowFactor and columnFactor for factor and multiply both with entry for transformedEntry.
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.
Multiply rowFactor and columnFactor for factor and multiply both with entry for transformedEntry.
When to use this tool
Use Matrix Diagonal Congruence Entry Factor when you need one transparent matrix-update component.
How to use the tool and how it works
- Enter entry, rowFactor, columnFactor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read factor, transformedEntry. Use the output convention below.
Multiply rowFactor and columnFactor for factor and multiply both with entry for transformedEntry.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entry | Entry | Required. Finite number. |
| rowFactor | Row Factor | Required. Finite number. |
| columnFactor | Column Factor | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| factor | Factor | Required. Finite number. |
| transformedEntry | Transformed Entry | Required. Finite number. |
{
"input": {
"entry": 3,
"rowFactor": 2,
"columnFactor": 4
},
"output": {
"factor": 8,
"transformedEntry": 24
}
}Limitations and assumptions
- This gives one real diagonal congruence entry; no invertibility or global matrix property is checked.
- 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 Similarity One Entry Factor
Require nonzero rowScale and columnScale and return entry × columnScale / rowScale.
- Matrix One Entry Rank One Update
Add weight × leftFactor × rightFactor to entry for one entry of a rank-one update.