Description
Return ij/2 + ji/2 as symmetric and ij/2 - ji/2 as skew.
A real matrix splits into symmetric and skew-symmetric parts by pairing transposed entries. Pairwise residuals test one relationship rather than the entire matrix.
Return ij/2 + ji/2 as symmetric and ij/2 - ji/2 as skew.
When to use this tool
Use Matrix Symmetric Skew Entry Split when you need one transposed-entry decomposition or residual.
How to use the tool and how it works
- Enter ij, ji. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read symmetric, skew. Use the output convention below.
Return ij/2 + ji/2 as symmetric and ij/2 - ji/2 as skew.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ij | Ij | Required. Finite number. |
| ji | Ji | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| symmetric | Symmetric | Required. Finite number. |
| skew | Skew | Required. Finite number. |
json
{
"input": {
"ij": 3,
"ji": 7
},
"output": {
"symmetric": 5,
"skew": -2
}
}Limitations and assumptions
- The pair is a real transpose decomposition, not a complex conjugate-transpose decomposition or a whole-matrix symmetry test.
- 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
Check all relevant entries with a documented scale-aware tolerance for numerical symmetry decisions.
References
Similar or alternative tools
- Matrix Skew Entry Pair Residual
Add aij and aji for the residual from skew symmetry.
- Matrix Packed Skewsign Alias
Map a coordinate to the upper pair min(row, column), max(row, column).