Description
Return one on the diagonal, zero above it, and storedValue below it.
Triangular storage can leave structural zeros and unit diagonals implicit. Solving or inverting requires usable diagonal entries, but a diagonal threshold alone does not measure conditioning.
Return one on the diagonal, zero above it, and storedValue below it.
When to use this tool
Use Matrix Unit Lower Entry Implicit Value when you need a triangular-entry convention or pivot diagnostic.
How to use the tool and how it works
- Enter row, column, storedValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value, implicit. Inspect implicit before interpreting the associated values.
Return one on the diagonal, zero above it, and storedValue below it. Mark implicit for diagonal and upper entries.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Safe integer; minimum 0. |
| column | Column | Required. Safe integer; minimum 0. |
| storedValue | Stored Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
| implicit | Implicit | Required. Boolean. |
{
"input": {
"row": 2,
"column": 2,
"storedValue": 9
},
"output": {
"value": 1,
"implicit": true
}
}Limitations and assumptions
- Indices are nonnegative but no matrix size is supplied; this represents a unit-lower storage convention rather than reading a matrix.
- 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 stable triangular solver and a condition estimate for a complete numerical solution.
References
Similar or alternative tools
- Matrix Triangular Diagonal Inverse Entry
Require a nonzero diagonal value and return its reciprocal.
- Matrix Triangular Solve Diagonal Flag
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.