PYTHON  Import the green channel of the following image URL (make sure your code works for this URL):  https://raw.githubusercontent.com/dpploy/chen-3170/master/notebooks/images/nerve-cells.jpg as a matrix A intended for linear algebra operations and show the matrix as an image as below (make sure the data is normalized). Show the complete data type specification of the matrix including maximum, minimum, average, and standard deviation values.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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PYTHON 

Import the green channel of the following image URL (make sure your code works for this URL):

 https://raw.githubusercontent.com/dpploy/chen-3170/master/notebooks/images/nerve-cells.jpg

as a matrix A intended for linear algebra operations and show the matrix as an image as below (make sure the data is normalized). Show the complete data type specification of the matrix including maximum, minimum, average, and standard deviation values.

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Compute the LU factorization of the symmetric part of A(100*100)and verify that your factorization is correct; explain. The symmetric part of a matrix sym(A) is defined as

sym(A) =( A+ A^T)/2
 Make your best visual demonstration (art contest) that it (the sym(A)
 matrix) is indeed symmetric.

The LU factorization program code is :

def lu_factorization(A):

2  """

3  Performs LU factorization of a matrix A without pivoting.

4

5  Args:

6    A: A square matrix.

7

8  Returns:

9    A tuple (L, U) where L is the lower triangular matrix and U is the upper triangular matrix.

10  """

11  n = len(A)

12  L = [[0.0] * n for _ in range(n)]

13  U = [[0.0] * n for _ in range(n)]

14

15  for k in range(n - 1):

16    for i in range(k + 1, n):

17

18      mik = A[i][k] / A[k][k]

19      L[i][k] = mik

20

21      for j in range(k + 1, n):

22        A[i][j] = A[i][j] - mik * A[k][j]

23

24      U[k][i] = mik

25

26  for i in range(n):

27    L[i][i] = 1.0

28

29  return L, U

30

31A = [[1.0, 2.0, 3.0],

32     [4.0, 5.0, 6.0],

33     [7.0, 8.0, 9.0]]

34

35L, U = lu_factorization(A)

36

37print("L:")

38for row in L:

39  print(row)

40

41print("U:")

42for row in U:

43  print(row)

 

 

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