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 through binary exponentiation. The signal is building the transition matrix and squaring it. Here is the answer.
Updated Sep 2026 · Grounded in real GenAI, LLM, and AI/ML engineering interview loops and written to a senior-engineer editorial bar.
Matrix exponentiation evaluates linear recurrences like Fibonacci at index n in O(log n) by raising a transition matrix to the nth power through binary exponentiation. The signal is building the transition matrix and squaring it. Here is the answer.
Lead with where the obvious approach breaks, because that is the judgment they are screening for — most candidates jump straight to the happy path and lose the room.
Then walk the failure back through the pipeline in order, naming the one metric the customer's exec sponsor actually cares about before you propose the fix.
