Matrix exponentiation: compute the nth term of a linear recurrence in O(log n).

Matrix exponentiation evaluates linear recurrences like Fibonacci at index n in O(log n) by raising a transition matrix to the nth power via binary exponentiation. The signal is building the transition matrix and squaring it. Here is the answer.

Updated Aug 2026 · Grounded in real Applied AI Engineer interview loops and written to a senior-engineer editorial bar.