Space complexity of matrix multiplication

1. What is the space complexity of matrix multiplication?
2. What is the complexity of multiplication?
3. What is the time complexity of matrix multiplication using divide and conquer?
4. How to calculate time complexity of matrix chain multiplication?

What is the space complexity of matrix multiplication?

Space Complexity

A new matrix is used to store the result of the multiplication. So, the space complexity is O(N^2).

What is the complexity of multiplication?

Hence, we know that multiplication has a time complexity of O(N logN) while usual algorithms in practice have a time complexity of O(N^2).

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.

How to calculate time complexity of matrix chain multiplication?

Time Complexity - We are using three nested for loops, each of which is iterating roughly O ( n ) O(n) O(n) times. Hence, the overall time complexity is O ( n 3 ) O(n^3) O(n3).