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

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