Discussion
Let A and B be two \(n \times n\) matrices. The efficient algorithm to multiply the two matrices has the time complexity
Answer: B
The efficient algorithm for multiplying two \(n \times n\) matrices listed here has complexity \(O(n^{2.81})\), which is Strassen's algorithm. It uses 7 multiplications of half-size matrices instead of 8, giving \(O(n^{\log_{2} 7}) = O(n^{2.81})\).
\(O(n^{3})\) is the ordinary method, so it is not the efficient one. \(O(n^{2.67})\) is not a known result in this list, and \(O(n^{2})\) is the trivial lower bound, which no known algorithm achieves.
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