Raise a matrix to the power of n by repeated multiplication
Matrix powers are computed by repeated multiplication. A^n means multiply A by itself n times, so A^2 is A times A and A^3 is A times A times A. Use this tool for queries such as matrix to the power of 2, matrix to the power of n, matrices raised to a power, and general matrix powers.
To raise a square matrix to a positive integer power, multiply the matrix by itself repeatedly. For example, A^4 = A x A x A x A. The exponent must be a non-negative integer in this calculator, and the matrix must be square so multiplication dimensions match.
Matrix power A^n is just multiplying A by itself n times. A^0 is the identity matrix, A^1 is A itself, A^2 is A×A, and so on. This is used in Markov chains, recurrence relations, and many other applications.
Any matrix to the 0 power is identity matrix I.
A^n = A multiplied n times in sequence.
Only square matrices can be raised to powers.
For diagonal D, D^n just powers each diagonal entry.
| Case | Rule | Meaning |
|---|---|---|
| A^0 | Identity matrix I | Works for any square matrix. |
| A^1 | A | The matrix stays unchanged. |
| A^2 | A x A | The most common matrix square query. |
| A^n | Repeated multiplication | Used for Markov chains, recurrences, and repeated transformations. |
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