Find minor matrix in python Code Answer

def getMatrixMinor(m,i,j):
    return [row[:j] + row[j+1:] for row in (m[:i]+m[i+1:])]

The above is the code that I find on the stack overflow in order to find the inverse of a matrix, however, I am really new in python. Can anybody explain the behind mechanism in order to construct a matrix of minor by using this code?

By the way, I’ve used this code and it works but I just don’t understand how it works.

Answer

Let’s start with the definition of (i,j)th minor matrix of a matrix:

(i,j)th minor of a matrix of size n is a smaller matrix of size n-1 with the i'th row and j'th column deleted.

Now lets look at this python one liner:

[row for row in (m[:i] + m[i+1:])]

m[:i] gives the first i rows of m (remember that we are representing a matrix as a list of rows, and adding two lists gives back a bigger list in python), now let’s look at another one liner:

row[:j] + row[j+1:]

This gives us all the elements of a row except the j'th element (lst[a:b] gives a list with elements from lst between a and b, with b excluded)

Combine the above two and you get an expression which returns a new matrix with i'th row and j'th column excluded:

def getMatrixMinor(m,i,j):
    return [row[:j] + row[j+1:] for row in (m[:i]+m[i+1:])]

Which is the minor matrix.