Dynamic programming | matrix multiplication

problem ：

1、 Problem analysis

The matrix multiplication problem is for a given n A matrix of continuous multiplication , Find a way to add parentheses , Minimize the even quantity of matrix multiplication .

（1） So what is matrix multiplicative ？

If two matrices , The first 1 The column of the first matrix is equal to 2 Row time of matrix , Then these two matrices are multiplicative , If 4-41 Shown .

（2） What is the result of matrix multiplication ？

The result matrix of multiplication of multiple matrices , The line is 、 The columns are equal to 1 Rows of a matrix 、 Last 1 Columns of a matrix , Pictured 4-41 Shown .

（3） How many times does it take to multiply two matrices ？

For example, two matrices A(3x2)、B(2x4)
Multiply , The execution process is as shown in the figure 4-43 Shown , Then we will execute it altogether 3 * 2 * 4 = 24 Secondary multiplication . therefore ,A(mxn)