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Linear Algebra Project

Description

This project focuses on understanding and applying basic linear algebra concepts using Python. It involves vector and matrix operations, including slicing, element-wise operations, concatenation, and matrix multiplication, leveraging the NumPy library.

External Resources

References

Learning Objectives

At the end of this project, you are expected to be able to explain to anyone, without the help of Google:

  • What is a vector?
  • What is a matrix?
  • What is a transpose?
  • What is the shape of a matrix?
  • What is an axis?
  • What is a slice?
  • How do you slice a vector/matrix?
  • What are element-wise operations?
  • How do you concatenate vectors/matrices?
  • What is the dot product?
  • What is matrix multiplication?
  • What is Numpy?
  • What is parallelization and why is it important?
  • What is broadcasting?

Concepts Covered

  • Vectors and matrices
  • Transpose and shape of a matrix
  • Element-wise operations
  • Matrix multiplication and dot product
  • NumPy library usage

Requirements

Python Scripts

  • Allowed editors: vi, vim, emacs
  • All your files will be interpreted/compiled on Ubuntu 20.04 LTS using python3 (version 3.9)
  • Your files will be executed with numpy (version 1.25.2)
  • All your files should end with a new line
  • The first line of all your files should be exactly #!/usr/bin/env python3
  • A README.md file, at the root of the folder of the project, is mandatory
  • Your code should follow pycodestyle (version 2.11.1)
  • All your modules should have documentation (python3 -c 'print(import("my_module").doc)')
  • All your classes should have documentation (python3 -c 'print(import("my_module").MyClass.doc)')
  • All your functions (inside and outside a class) should have documentation (python3 -c 'print(import("my_module").my_function.doc)' and python3 -c 'print(import("my_module").MyClass.my_function.doc)')
  • Unless otherwise noted, you are not allowed to import any module
  • All your files must be executable
  • The length of your files will be tested using wc

Tasks

  1. Slice Me Up - Slicing arrays in various ways. Complete the following source code (found below):
  • arr1 should be the first two numbers of arr
  • arr2 should be the last five numbers of arr
  • arr3 should be the 2nd through 6th numbers of arr
  • You are not allowed to use any loops or conditional statements
  • Your program should be exactly 8 lines

The program should consist of exactly 8 lines.

alexa@ubuntu-xenial:linear_algebra$ cat 0-slice_me_up.py 
#!/usr/bin/env python3
arr = [9, 8, 2, 3, 9, 4, 1, 0, 3]
arr1 =  # your code here
arr2 =  # your code here
arr3 =  # your code here
print("The first two numbers of the array are: {}".format(arr1))
print("The last five numbers of the array are: {}".format(arr2))
print("The 2nd through 6th numbers of the array are: {}".format(arr3))
alexa@ubuntu-xenial:linear_algebra$ ./0-slice_me_up.py 
The first two numbers of the array are: [9, 8]
The last five numbers of the array are: [9, 4, 1, 0, 3]
The 2nd through 6th numbers of the array are: [8, 2, 3, 9, 4]
alexa@ubuntu-xenial:linear_algebra$ wc -l 0-slice_me_up.py 
8 0-slice_me_up.py
alexa@ubuntu-xenial:linear_algebra$

Repo:

  • GitHub repository: holbertonschool-machine_learning
  • Directory: math/linear_algebra
  • File: 0-slice_me_up.py
  1. Trim Me Down - Extracting specific columns from a matrix. Complete the following source code (found below):
  • the_middle should be a 2D matrix containing the 3rd and 4th columns of matrix
  • You are not allowed to use any conditional statements
  • You are only allowed to use one for loop
  • Your program should be exactly 6 lines
alexa@ubuntu-xenial:linear_algebra$ cat 1-trim_me_down.py 
#!/usr/bin/env python3
matrix = [[1, 3, 9, 4, 5, 8], [2, 4, 7, 3, 4, 0], [0, 3, 4, 6, 1, 5]]
the_middle = []
# your code here
print("The middle columns of the matrix are: {}".format(the_middle))
alexa@ubuntu-xenial:linear_algebra$ ./1-trim_me_down.py 
The middle columns of the matrix are: [[9, 4], [7, 3], [4, 6]]
alexa@ubuntu-xenial:linear_algebra$ wc -l 1-trim_me_down.py 
6 1-trim_me_down.py
alexa@ubuntu-xenial:linear_algebra$

Repo:

  • GitHub repository: holbertonschool-machine_learning
  • Directory: math/linear_algebra
  • File: 1-trim_me_down.py
  1. Size Me Please - Calculating the shape of a matrix. Write a function def matrix_shape(matrix): that calculates the shape of a matrix:
  • You can assume all elements in the same dimension are of the same type/shape
  • The shape should be returned as a list of integers
alexa@ubuntu-xenial:linear_algebra$ cat 2-main.py 
#!/usr/bin/env python3

matrix_shape = __import__('2-size_me_please').matrix_shape

mat1 = [[1, 2], [3, 4]]
print(matrix_shape(mat1))
mat2 = [[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]],
        [[16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30]]]
print(matrix_shape(mat2))
alexa@ubuntu-xenial:linear_algebra$ ./2-main.py 
[2, 2]
[2, 3, 5]
alexa@ubuntu-xenial:linear_algebra$

Repo:

  • GitHub repository: holbertonschool-machine_learning
  • Directory: math/linear_algebra
  • File: 2-size_me_please.py
  1. Flip Me Over - Transposing a matrix. Write a function def matrix_transpose(matrix): that returns the transpose of a 2D matrix, matrix:
  • You must return a new matrix
  • You can assume that matrix is never empty
  • You can assume all elements in the same dimension are of the same type/shape
alexa@ubuntu-xenial:linear_algebra$ cat 3-main.py 
#!/usr/bin/env python3

matrix_transpose = __import__('3-flip_me_over').matrix_transpose

mat1 = [[1, 2], [3, 4]]
print(mat1)
print(matrix_transpose(mat1))
mat2 = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15],
        [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30]]
print(mat2)
print(matrix_transpose(mat2))
alexa@ubuntu-xenial:linear_algebra$ ./3-main.py 
[[1, 2], [3, 4]]
[[1, 3], [2, 4]]
[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30]]
[[1, 6, 11, 16, 21, 26], [2, 7, 12, 17, 22, 27], [3, 8, 13, 18, 23, 28], [4, 9, 14, 19, 24, 29], [5, 10, 15, 20, 25, 30]]
alexa@ubuntu-xenial:linear_algebra$

Repo:

  • GitHub repository: holbertonschool-machine_learning
  • Directory: math/linear_algebra
  • File: 3-flip_me_over.py
  1. Line Up - Adding two arrays element-wise. Write a function def add_arrays(arr1, arr2): that adds two arrays element-wise:
  • You can assume that arr1 and arr2 are lists of ints/floats
  • You must return a new list
  • If arr1 and arr2 are not the same shape, return None
alexa@ubuntu-xenial:linear_algebra$ cat 4-main.py 
#!/usr/bin/env python3

add_arrays = __import__('4-line_up').add_arrays

arr1 = [1, 2, 3, 4]
arr2 = [5, 6, 7, 8]
print(add_arrays(arr1, arr2))
print(arr1)
print(arr2)
print(add_arrays(arr1, [1, 2, 3]))
alexa@ubuntu-xenial:linear_algebra$ ./4-main.py 
[6, 8, 10, 12]
[1, 2, 3, 4]
[5, 6, 7, 8]
None
alexa@ubuntu-xenial:linear_algebra$

Repo:

  • GitHub repository: holbertonschool-machine_learning
  • Directory: math/linear_algebra
  • File: 4-line_up.py
  1. Across The Planes - Adding two matrices element-wise. Write a function def add_matrices2D(mat1, mat2): that adds two matrices element-wise:
  • You can assume that mat1 and mat2 are 2D matrices containing ints/floats
  • You can assume all elements in the same dimension are of the same type/shape
  • You must return a new matrix
  • If mat1 and mat2 are not the same shape, return None
  1. Howdy Partner - Concatenating two arrays.
  2. Gettin’ Cozy - Concatenating two matrices along a specific axis.
  3. Ridin’ Bareback - Performing matrix multiplication.
  4. Let The Butcher Slice It - Complex slicing on matrices.
  5. I’ll Use My Scale - Determining the shape of a NumPy array.
  6. The Western Exchange - Transposing a NumPy array.
  7. Bracing The Elements - Element-wise operations on NumPy arrays.
  8. Cat's Got Your Tongue - Concatenating NumPy arrays along a specific axis.
  9. Saddle Up - Matrix multiplication using NumPy.
  10. Slice Like A Ninja (Advanced) - Advanced slicing techniques on NumPy arrays.
  11. The Whole Barn (Advanced) - Adding matrices of varying dimensions.
  12. Squashed Like Sardines (Advanced) - Advanced matrix concatenation.

This README is under construction.