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Matrix Rank — result sheet
Estimate the numerical rank of a finite row-major 3x3 matrix with a documented scale-relative pivot tolerance.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: rank(A) is the number of pivots retained by partial-pivot elimination after treating pivots at or below 1e-12 times max(abs(Aij)) as zero.
The rank is the number of numerically independent pivot rows or columns in the entered 3x3 matrix. This implementation uses partial-pivot elimination and states its scale-relative tolerance instead of parsing an arbitrary matrix expression.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- A11 — matrix entry; Row 1, column 1 of matrix A.; minimum -1000; maximum 1000
- A12 — matrix entry; Row 1, column 2 of matrix A.; minimum -1000; maximum 1000
- A13 — matrix entry; Row 1, column 3 of matrix A.; minimum -1000; maximum 1000
- A21 — matrix entry; Row 2, column 1 of matrix A.; minimum -1000; maximum 1000
- A22 — matrix entry; Row 2, column 2 of matrix A.; minimum -1000; maximum 1000
- A23 — matrix entry; Row 2, column 3 of matrix A.; minimum -1000; maximum 1000
- A31 — matrix entry; Row 3, column 1 of matrix A.; minimum -1000; maximum 1000
- A32 — matrix entry; Row 3, column 2 of matrix A.; minimum -1000; maximum 1000
- A33 — matrix entry; Row 3, column 3 of matrix A.; minimum -1000; maximum 1000
Worked example
| Input | Value |
|---|---|
| A11 | 1 |
| A12 | 2 |
| A13 | 3 |
| A21 | 0 |
| A22 | 1 |
| A23 | 4 |
| A31 | 5 |
| A32 | 6 |
| A33 | 0 |
Partial-pivot elimination retains three pivots, so rank(A) = 3.
Assumptions and limits
- A is a real 3x3 matrix supplied through the fixed row-major numeric fields.
- Each entry is finite and bounded from -1000 through 1000 inclusive.
- Numerical rank uses partial-pivot elimination with relative tolerance 1e-12 times the largest absolute matrix entry; a zero matrix has rank 0.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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