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Matrix Transpose — result sheet
Transpose a finite row-major 3x3 matrix by exchanging its row and column indices.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (A transpose)ij = Aji, so each row and column index is exchanged.
Transposition reflects a square matrix across its main diagonal. It preserves every entry and changes only its row-column position, producing a deterministic 3x3 text matrix.
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 |
A^T = [[1, 0, 5], [2, 1, 6], [3, 4, 0]].
Assumptions and limits
- A is a real 3x3 matrix entered in fixed row-major order.
- All nine entries are finite numbers between -1000 and 1000 inclusive.
- The operation is a structural transpose only; no conjugation, sorting, scaling, or unit interpretation is applied.
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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