Find minor matrix in python

Question

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.

I know that row[:j] is getting all element from index 0 to before j(excluded j) and row[j+1:] is getting all the element form j+1 to the rest. Is it correct? — Thanakorn Pasangthien Ming, Dec 26 '18 at 16:36

score 2 · Accepted Answer · answered Dec 26 '18 at 18:58

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.

Thanks for the advice I just started to use StackOverflow for real by sign up to the site just two days ago. — Thanakorn Pasangthien Ming, Dec 28 '18 at 17:21

score 0 · Answer 2 · answered Dec 26 '18 at 18:46

The function is very simple, used to compute the first minor matrices. Suppose you have a squared matrix of size m x m, and you want to compute the first minor matrix at position (i,j), what do you do? You have to extract a smaller matrix of size (m-1) x (m-1) from the original matrix by removing the row i-th and the column j-th, which is done by the function.

Concretely, m[:i]+m[i+1:] removes the i-th row and creates a new list of the remaining rows. For each row in this list, the function remove the element row[j]. The output of the function is a list of lists (rows) representing the corresponding minor matrix.

I recommend you to have a look at Python list comprehension and list slicing.

Thank you so much sir, very much appreciated. – Thanakorn Pasangthien Ming Dec 27 '18 at 06:02 — Thanakorn Pasangthien Ming, Dec 27 '18 at 06:02

GoAl · Answer 3 · 2021-11-14T13:36:36.410

0

Maybe it will be useful for somebody, just want to share with you my working solution, any constructive critic is acceptable

def getMatrixMinor(arr,i,j):
    c = arr[:]
    c = np.delete(c, (i),axis=0)
    return [np.delete(row, (j),axis=0) for row in (c)]

As practical example you can see my implementation here based on this function for determinant calculation.

edited Nov 14 '21 at 13:36

answered Dec 23 '20 at 18:18

GoAl

1
1

score -1 · Answer 4 · answered Jun 15 '21 at 11:28

# Finding minors of a matrix and it's determinant

import numpy as np
from numpy import *

n = 4
arr = random.randint(0,10,(n,n))
print(arr)

def getMatrixMinor(arr,i,j):
    c = arr[:]
    c_r = np.delete(c, (i),axis=0) # deletes i-th row
    c_c = np.delete(c_r, (j),axis=1) #deletes j-th column
    return c_c

gmm = getMatrixMinor(arr,2,2)
print("gmm = \n",gmm)

d = linalg.det(gmm)
print("d =",d)

    [[6 3 4 6]
     [0 8 5 2]
     [2 9 6 3]
     [6 5 2 1]]
    gmm = 
     [[6 3 6]
     [0 8 2]
     [6 5 1]]
     d = -263.99999999999994,
     
     Thanks GoAI, mine is a slight change from your answer.

Please add some text outside of the code block which actually answers the question *"...Can anybody explain..."*. — trincot, Jun 15 '21 at 17:24

Find minor matrix in python

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