Description
Multiply coordinate by productCoordinate and divide by positive squaredNorm.
Matrix-product entries are dot products of matching rows and columns. Trace and Rayleigh-quotient contributions require corresponding coordinates from the same underlying calculation.
Multiply coordinate by productCoordinate and divide by positive squaredNorm.
When to use this tool
Use Matrix Rayleigh One Coordinate Term when you need one explicit real matrix-product contribution.
How to use the tool and how it works
- Enter coordinate, productCoordinate, squaredNorm. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Multiply coordinate by productCoordinate and divide by positive squaredNorm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
| productCoordinate | Product Coordinate | Required. Finite number. |
| squaredNorm | Squared Norm | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | Contribution | Required. Finite number. |
{
"input": {
"coordinate": 2,
"productCoordinate": 6,
"squaredNorm": 4
},
"output": {
"contribution": 3
}
}Limitations and assumptions
- The inputs must come from the same vector and matrix-vector product; this is one real Rayleigh-quotient summand, not the full quotient.
- 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
Validate complete shapes and coordinate correspondence before aggregating contributions or using a matrix library.
References
Similar or alternative tools
- Matrix: Matrix Block Local Coordinate
Check membership in the half-open row and column ranges of the block.
- Matrix Block Transpose Coordinate Map
Split column by blockColumns for transposed blockRow and localRow, and split row by blockRows for blockColumn and localColumn.