Hướng dẫn php matrix operations

Given two matrices, the task to multiply them. Matrices can either be square or rectangular.

Examples: 

Input : mat1[][] = {{1, 2}, 
                   {3, 4}}
        mat2[][] = {{1, 1}, 
                    {1, 1}}
Output : {{3, 3}, 
          {7, 7}}
Input : mat1[][] = {{2, 4}, 
                    {3, 4}}
        mat2[][] = {{1, 2}, 
                    {1, 3}}       
Output : {{6, 16}, 
          {7, 18}}

Multiplication of Square Matrices : 
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions. 

PHP

Output

Result matrix is 
10 10 10 10 
20 20 20 20 
30 30 30 30 
40 40 40 40

Time complexity: O[n3]. It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O[n2]

Multiplication of Rectangular Matrices : 
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C? 

PHP

Time complexity: O[n3]. It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O[m1 * n2]

Please refer complete article on Program to multiply two matrices for more details!