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Matrix Trace — result sheet
Sum the three main-diagonal entries of a finite row-major 3x3 matrix.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: tr(A) = a11 + a22 + a33.
The trace is the scalar sum of the main diagonal of a square matrix. For this fixed 3x3 contract, only a11, a22, and a33 contribute to the numeric result.
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 |
tr(A) = 1 + 1 + 0 = 2.
Assumptions and limits
- A is a finite real 3x3 matrix in fixed row-major order.
- All nine entries are bounded from -1000 through 1000 inclusive, even though off-diagonal entries do not affect the trace.
- The result is a scalar arithmetic metric and does not infer eigenvalues, units, or a physical interpretation.
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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