Certainly! In the performance analysis, we compared the execution times of sequential matrix multiplication and parallel matrix multiplication for different matrix sizes (100x100, 200x200, 400x400, and 800x800) and varying numbers of processes (2, 4, 6, and 8).

For each matrix size, we measured the sequential execution time, which represents the time taken by the traditional sequential approach. Then, we measured the execution time for the parallel approach with different numbers of processes.

To evaluate the performance improvement achieved by the parallel implementation, we calculated the speedup. Speedup is the ratio of the sequential execution time to the parallel execution time. Higher speedup values indicate better performance.

By analyzing the speedup values for different matrix sizes and numbers of processes, we can determine the level of performance improvement achieved by the parallel implementation. The parallel approach should ideally result in higher speedup values compared to the sequential approach.

Other metrics such as efficiency and scalability can also be considered. Efficiency measures how effectively the parallel implementation utilizes the available resources and is calculated as the ratio of speedup to the number of processes. Scalability refers to the ability of the parallel implementation to maintain or improve performance as the problem size or the number of processes increases.

Analyzing these metrics across different matrix sizes and numbers of processes helps us understand the performance improvement achieved by the parallel implementation of matrix multiplication.