I have a general question
For example we have matrix M1 and mattix M2, 2x2 both
I wanna do the product m2m1m1m2m2m1m1m2
Is there a shortcut like factorising?
Can you give me some basic rules about these please?
Thank you
When performing matrix multiplication, there are a few rules to keep in mind. However, there is no general shortcut like factorizing when you have a long chain of matrix multiplications. You will need to multiply the matrices in the given order to obtain the desired result.
Here are some basic rules for matrix multiplication:
1. The dimensions must be compatible: For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In your case, since both matrices M1 and M2 are 2x2, the dimensions are compatible.
2. Multiplication of two matrices: To multiply two matrices, each element in the resulting matrix is obtained by taking the dot product of the corresponding row of the first matrix and the corresponding column of the second matrix. For example, if M1 is multiplied by M2, the resulting matrix will have its (i,j) element as the dot product of the i-th row of M1 and the j-th column of M2.
3. Associative property: Matrix multiplication is associative, which means that when you have a chain of matrix multiplications, the result does not depend on the order in which you multiply the matrices. However, the sequence of multiplication matters. In your case, M2M1M1M2M2M1M1M2 would mean you multiply M2 with M1, then multiply the result by M1, then multiply the result by M2, and so on.
To compute the product M2M1M1M2M2M1M1M2, you need to carry out the matrix multiplications in the given order, following the rules mentioned above. There is no general shortcut or factorization technique to simplify the process.