Description
Require a nonzero diagonal value and return its reciprocal.
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.
Require a nonzero diagonal value and return its reciprocal.
When to use this tool
Use Matrix Triangular Diagonal Inverse Entry when you need a triangular-entry convention or pivot diagnostic.
How to use the tool and how it works
- Enter diagonal. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read inverse. Use the output convention below.
Require a nonzero diagonal value and return its reciprocal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diagonal | Diagonal | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| inverse | Inverse | Required. Finite number. |
json
{
"input": {
"diagonal": 4
},
"output": {
"inverse": 0.25
}
}Limitations and assumptions
- This gives an inverse diagonal entry for a triangular matrix; other inverse entries and near-singularity are not evaluated.
- 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 Solve Diagonal Flag
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.
- Matrix 2x2 Schur Complement Scalar
Require a nonzero a and return d - c × b / a for the scalar Schur complement.