Calculate matrix powers An with efficient algorithms and step-by-step visualization.
Matrix Exponentiation:
An means multiplying matrix A by itself n times. For n=0, result is identity matrix I.
Special Cases:
Applications:
Efficiency:
For large n, this calculator uses repeated squaring: O(log n) multiplications instead of O(n).
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Matrix exponentiation multiplies a square matrix by itself n times. This tool uses efficient repeated squaring (O(log n)) and optimizations for diagonal, idempotent, and nilpotent cases. Special case: A^0 = I.
Markov chains (long‑run behavior), graph theory (path counts via adjacency powers), linear recurrences (e.g., Fibonacci), repeated geometric transforms, and systems of differential equations.
Supports square matrices and integer exponents in a practical range (including 0). For large n, repeated squaring keeps computations fast and stable.