Matrix Power Calculator

Compute A to the power n by repeated multiplication for a 2x2 or 3x3 square matrix with non-negative integer exponent (0 through 50).

Frequently Asked Questions

How is A to the power n computed?

By repeated matrix multiplication, accelerated by exponentiation by squaring. For diagonalizable A, the formula A equals P D to the n times P inverse is much faster than direct multiplication for large n.

Can I use a negative or fractional exponent?

Not here. Negative exponents require the inverse first. Fractional matrix powers (matrix square root, etc.) are not unique and need SVD or spectral decomposition.

What is A to the power zero?

The identity matrix I, regardless of A (as long as A is square). This matches the scalar convention that any nonzero number raised to the zero is one.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.