Matrix Power Calculator
Raise a square matrix to a non-negative integer power n. A^0 returns the identity matrix; A^1 returns A itself.
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Notes
Matrix Powers
The n-th power of a square matrix A is A multiplied by itself n times. The matrix must be square.
Example: A²
A:
| 1 | 2 |
| 3 | 4 |
A² = A · A:
| 7 | 10 |
| 15 | 22 |
(1·1+2·3=7, 1·2+2·4=10, 3·1+4·3=15, 3·2+4·4=22)
A^0 = I (identity matrix) by convention. This calculator uses fast exponentiation (binary method) to handle large powers efficiently.
See also
- Matrix Calculations Guide — Matrix Multiplication & Powers — In-depth notes on Matrix Multiplication & Powers with worked examples
Frequently Asked Questions
What is A^0?
A^0 equals the identity matrix I of the same size as A. This is the convention for all square matrices.
Can I compute a negative power?
A^(−n) = (A⁻¹)^n. This calculator handles non-negative powers only; use the Matrix Inverse calculator first if needed.
How does the determinant behave under matrix powers?
det(A^n) = det(A)^n. So if det(A) = 2, then det(A³) = 8.