Matrix matrix multiplication complexity

1. What time complexity is matrix multiplication?
2. What is the time complexity of matrix multiplication using divide and conquer?
3. What is the time complexity of matrix chain multiplication *?
4. What is Big O complexity of brute force matrix multiplication?

What time complexity is matrix multiplication?

As of October 2022, the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n^2.37188) time, given by Duan, Wu and Zhou announced in a preprint.

What is the time complexity of matrix multiplication using divide and conquer?

The Divide and Conquer algorithm solves the problem in O(nLogn) time. Strassen's Algorithm is an efficient algorithm to multiply two matrices. A simple method to multiply two matrices need 3 nested loops and is O(n^3) . Strassen's algorithm multiplies two matrices in O(n^2.8974) time.

What is the time complexity of matrix chain multiplication *?

However the matrix chain multiplication is a dynamic programming paradigm and takes O(n³) computational complexity.

What is Big O complexity of brute force matrix multiplication?

The Brute force Time Complexity of Multiplication operation is O(logM x logM) while the Theoretical limit of Time Complexity of Multiplication operation is O(logM x loglogM) for multiplying number number M x M.