Description
Compare one pair of transposed matrix-entry values.
Matrix indices depend on whether counting begins at zero or one and on the direction of row/column offsets. Comparing a transposed entry pair is one local symmetry check. Supplied index arithmetic does not establish matrix dimensions, valid element membership or a global algebraic property.
Compare one pair of transposed matrix-entry values.
When to use this tool
Use Matrix Symmetric Entry Pair Residual when you already have entryIJ, entryJI and need to compare one pair of transposed matrix-entry values.
How to use the tool and how it works
- Enter entryIJ, entryJI. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedGap. Use the output convention below.
Return entryJI-entryIJ.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entryIJ | Entry IJ | Required. Finite number. |
| entryJI | Entry JI | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedGap | Signed Gap | Required. Finite number. |
{
"input": {
"entryIJ": 12,
"entryJI": 17
},
"output": {
"signedGap": 5
}
}Limitations and assumptions
- Zero residual checks only this pair, not full matrix symmetry, dimensions, numerical tolerance or a matrix property proof.
- 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 actual matrix and its declared index convention when checking entries or a global property. Apply complete symmetry or structural checks with an explicit numerical tolerance when one pairwise residual is insufficient.
References
Similar or alternative tools
- Matrix One Based Index Crosswalk
Convert supplied row and column indices between zero- and one-based conventions.
- Matrix Diagonal Unit Offset
Calculate a diagonal offset and zero-based row/column indices.