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Matrix Power — result sheet
Raise a finite row-major 3x3 matrix to a bounded whole-number exponent from 0 through 12.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A^0 = I3; for n > 0, A^n is the ordered product of n copies of A, evaluated here by exponentiation by squaring.
Matrix power repeats ordered matrix multiplication for a whole-number exponent. The exponent is bounded for predictable arithmetic, and exponent zero is defined as the 3x3 identity 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
- Exponent — whole-number exponent; A whole number from 0 through 12; exponent zero means I3.; minimum 0; maximum 12
Worked example
| Input | Value |
|---|---|
| A11 | 1 |
| A12 | 2 |
| A13 | 3 |
| A21 | 0 |
| A22 | 1 |
| A23 | 4 |
| A31 | 5 |
| A32 | 6 |
| A33 | 0 |
| Exponent | 2 |
A^2 = [[16, 22, 11], [20, 25, 4], [5, 16, 39]].
Assumptions and limits
- A is a finite real 3x3 matrix in fixed row-major order.
- The exponent is an integer from 0 through 12 and every multiplication intermediate must stay finite within the bounded arithmetic range.
- A matrix power means repeated ordinary matrix multiplication; no elementwise powers, inverse powers, eigen-decomposition, or symbolic parsing is inferred.
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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