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Python | Linear Algebra

Linear Algebra is a branch of mathematics that deals with large data by the use of Vectors and Matrices. It introduces a different way of viewing and understanding large data. Matrices and Vectors are the primary tools and are used for data representations. A vector is also a unit column matrix. Linear Algebra can also be defined as "Mathematics of n-dimensional Space". It involves four subspaces:

1. Column Space
2. Row Space
3. Null Space
4. Left Null Space

There are multiple types of matrices and multiple operations that can be done on Matrices. In this learning sequence, we are going to use python to implement these matrices and how to manipulate them using different operations.

Why should we use Python?

• Python is a higher-level computer programming language. Apart from this, it provides a large number of packages (mainly numpy for matrices and vectors) which allow us to perform operations on big data very effectively as well as it is very efficacious.
• Python is being used almost everywhere. Python use in projects, software development, algorithmic programming/machine learning, and research made it one of the cardinal languages in computer science. Python provides a freehand for learning Linear Algebra so that you can implement it in any of the domains.

List of python programs in linear algebra

1. Defining a Vector using list
2. Defining Vector using Numpy
3. Vector with User Defined Length
4. Adding two vectors
5. Scalar Multiplication of Vector
6. Scalar Multiplication of Vector using NumPy
7. Scalar Multiplication Property 1
8. Scalar Multiplication Property 2
9. Adding Dimension to the Vector
10. Calling ith dimensional Component of Vector
11. Vector Magnitude using Function
12. Dot Product of Vectors
13. Cosine Similarity between two vectors
14. A Linear Function Vector
15. Random Integer Vector
16. Defining Matrix using Numpy
17. Creating a Matrix using Columns
18. Creating a Matrix using Rows
19. Calling Column of a Matrix
20. Calling Row of a Matrix
21. Matrix Addition
22. Row numbers in a Matrix
23. Scalar Multiplication of Matrix
24. Shape of Matrix
25. (i,j) Element from a Matrix
26. Calling Column of a Matrix using Function
27. Calling Row of a Matrix using Function
28. Checking Square Matrix
29. Python | Vandermonde Matrix
30. numpy.matmul( ) for Matrix Multiplication
31. Python | Constant Matrix
32. Python | Range of a Matrix
33. Python | Rank of a Matrix
34. Python | Trace of a Matrix
35. Python | Sign and Natural Logarithm of Determinant of a Matrix
36. Python | Diagonal of a Matrix
37. Python | Lower Triangle of a Matrix
38. Python | Upper Triangle of a Matrix
39. numpy.random.random( ) function with no input parameter
40. randomisation() Function to generate Random Vector
41. randomisation_matrix() Function to generate Random Matrix
42. Printing the power of vector/matrix elements using pow(x,a)
43. Printing sin value of vector/matrix elements using numpy.sin()
44. Printing hyperbolic tangent value of vector/matrix elements using numpy.tanh()
45. Printing Cosine value of vector/matrix (element wise operation)
46. Printing logarithmic value of vector/matrix (element wise operation)
47. Printing exponential value of vector/matrix elements using numpy.exp()
48. Print the identity matrix using numpy.eye() function
49. Identity Matrix Property (I^k = I)
50. Identity Matrix Property (AI = A)
51. Representation of a Linear Equation
52. Representation of a System of Linear Equation
53. Transpose Matrix
54. Identity Matrix Transpose Property
55. Symmetric Matrices
56. Creating Symmetric Matrices
57. Sum of Symmetric Matrices
58. Ones matrix using numpy.ones()
59. Zeros Matrix using numpy.zeros()
60. Determinant of a Matrix
61. Determinant of Identity Matrix
62. Determinant of a Transpose Matrix
63. Determinant of a Zeros and Ones matrices
64. Determinant of a non-square matrix
65. Inverse of a Matrix
66. Inverse of an Identity Matrix
67. Minimum value from a Matrix
68. Maximum value from a Matrix
69. Mean value from a Matrix
70. Product of a Matrix and its Inverse Property
71. Product of a Matrix and its Transpose Property
72. Comparing Maximum from Matrices
73. Comparing Minimum from Matrices
74. Norm of the Vector
75. Outer Product of Vectors
76. Outer Product Properties
77. Python | Application to School CPI Records (Linear Algebra)

Neural Network

1. Introduction to Simplest Neural Network
2. Uni - Layer Neural Network
3. Python | One Hidden Layer Simplest Neural Network

Application of Linear Algebra in Machine Learning

1. Hinge Loss for Single Point
2. Function for Hinge Loss for Single Point
3. Function for Hinge Loss for Multiple Points
4. Binomial Process
5. Python | Binomial Experiment Simulation
6. Euclidean Distance Example