线性代数 python_Python | 线性代数

本是古典何须时尚 2023-03-05 09:44 25阅读 0赞

线性代数 python

**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:

**线性代数**是数学的一个分支，它通过使用向量和矩阵来处理大数据。 它引入了查看和理解大数据的另一种方式。 矩阵和向量是主要工具，用于数据表示。 向量也是单位列矩阵。 线性代数也可以定义为“ n维空间数学”。 它涉及四个子空间：

1.  Column Space
    
    列空间
2.  Row Space
    
    行空间
3.  Null Space
    
    空空间
4.  Left Null Space
    
    左空空间

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.

有多种类型的矩阵和可以对矩阵执行的多种操作。 在此学习序列中，我们将使用python实现这些矩阵以及如何使用不同的操作来操纵它们。

**Why should we use Python?**

**为什么要使用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是高级计算机编程语言。 除此之外，它提供了大量的程序包(主要是矩阵和矢量的numpy程序包)，这些程序包使我们能够非常有效地对大数据执行操作，并且非常有效。
 *  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.
    
    几乎所有地方都在使用Python。 Python在项目，软件开发，算法编程/机器学习和研究中的使用使其成为计算机科学中的主要语言之一。 Python提供了学习线性代数的徒手画法，因此您可以在任何领域中实现它。

## 线性代数中的python程序列表 **(**List of python programs in linear algebra**)** ##

1.  [Defining a Vector using list][]
    
    [使用列表定义向量][Defining a Vector using list]
2.  [Defining Vector using Numpy][]
    
    [使用Numpy定义向量][Defining Vector using Numpy]
3.  [Vector with User Defined Length][]
    
    [用户定义长度的向量][Vector with User Defined Length]
4.  [Adding two vectors][]
    
    [两个向量相加][Adding two vectors]
5.  [Scalar Multiplication of Vector][]
    
    [向量的标量乘法][Scalar Multiplication of Vector]
6.  [Scalar Multiplication of Vector using NumPy][]
    
    [使用NumPy对向量进行标量乘法][Scalar Multiplication of Vector using NumPy]
7.  [Scalar Multiplication Property 1][]
    
    [标量乘法属性1][Scalar Multiplication Property 1]
8.  [Scalar Multiplication Property 2][]
    
    [标量乘法属性2][Scalar Multiplication Property 2]
9.  [Adding Dimension to the Vector][]
    
    [向向量添加维][Adding Dimension to the Vector]
10. [Calling ith dimensional Component of Vector][]
    
    [调用向量的第i维分量][Calling ith dimensional Component of Vector]
11. [Vector Magnitude using Function][]
    
    [使用功能的矢量幅度][Vector Magnitude using Function]
12. [Dot Product of Vectors][]
    
    [向量的点积][Dot Product of Vectors]
13. [Cosine Similarity between two vectors][]
    
    [两个向量之间的余弦相似度][Cosine Similarity between two vectors]
14. [A Linear Function Vector][]
    
    [线性函数向量][A Linear Function Vector]
15. [Random Integer Vector][]
    
    [随机整数向量][Random Integer Vector]
16. [Defining Matrix using Numpy][]
    
    [使用Numpy定义矩阵][Defining Matrix using Numpy]
17. [Creating a Matrix using Columns][]
    
    [使用列创建矩阵][Creating a Matrix using Columns]
18. [Creating a Matrix using Rows][]
    
    [使用行创建矩阵][Creating a Matrix using Rows]
19. [Calling Column of a Matrix][]
    
    [矩阵的调用列][Calling Column of a Matrix]
20. [Calling Row of a Matrix][]
    
    [调用矩阵的行][Calling Row of a Matrix]
21. [Matrix Addition][]
    
    [矩阵加法][Matrix Addition]
22. [Row numbers in a Matrix][]
    
    [矩阵中的行号][Row numbers in a Matrix]
23. [Scalar Multiplication of Matrix][]
    
    [矩阵的标量乘法][Scalar Multiplication of Matrix]
24. [Shape of Matrix][]
    
    [矩阵形状][Shape of Matrix]
25. [(i,j) Element from a Matrix][i_j_ Element from a Matrix]
    
    [(i，j)矩阵中的元素][i_j_ Element from a Matrix]
26. [Calling Column of a Matrix using Function][]
    
    [使用函数调用矩阵的列][Calling Column of a Matrix using Function]
27. [Calling Row of a Matrix using Function][]
    
    [使用函数调用矩阵的行][Calling Row of a Matrix using Function]
28. [Checking Square Matrix][]
    
    [检查平方矩阵][Checking Square Matrix]
29. [Python | Vandermonde Matrix][Python _ Vandermonde Matrix]
    
    [Python |][Python _ Vandermonde Matrix] [范德蒙矩阵][Python _ Vandermonde Matrix]
30. [numpy.matmul( ) for Matrix Multiplication][numpy.matmul_ _ for Matrix Multiplication]
    
    [numpy.matmul()用于矩阵乘法][numpy.matmul_ _ for Matrix Multiplication]
31. [Python | Constant Matrix][Python _ Constant Matrix]
    
    [Python |][Python _ Constant Matrix] [常数矩阵][Python _ Constant Matrix]
32. [Python | Range of a Matrix][Python _ Range of a Matrix]
    
    [Python |][Python _ Range of a Matrix] [矩阵范围][Python _ Range of a Matrix]
33. [Python | Rank of a Matrix][Python _ Rank of a Matrix]
    
    [Python |][Python _ Rank of a Matrix] [矩阵等级][Python _ Rank of a Matrix]
34. [Python | Trace of a Matrix][Python _ Trace of a Matrix]
    
    [Python |][Python _ Trace of a Matrix] [矩阵的痕迹][Python _ Trace of a Matrix]
35. [Python | Sign and Natural Logarithm of Determinant of a Matrix][Python _ Sign and Natural Logarithm of Determinant of a Matrix]
    
    [Python |][Python _ Sign and Natural Logarithm of Determinant of a Matrix] [矩阵行列式的符号和自然对数][Python _ Sign and Natural Logarithm of Determinant of a Matrix]
36. [Python | Diagonal of a Matrix][Python _ Diagonal of a Matrix]
    
    [Python |][Python _ Diagonal of a Matrix] [矩阵的对角线][Python _ Diagonal of a Matrix]
37. [Python | Lower Triangle of a Matrix][Python _ Lower Triangle of a Matrix]
    
    [Python |][Python _ Lower Triangle of a Matrix] [矩阵的下三角][Python _ Lower Triangle of a Matrix]
38. [Python | Upper Triangle of a Matrix][Python _ Upper Triangle of a Matrix]
    
    [Python |][Python _ Upper Triangle of a Matrix] [矩阵的上三角][Python _ Upper Triangle of a Matrix]
39. [numpy.random.random( ) function with no input parameter][numpy.random.random_ _ function with no input parameter]
    
    [没有输入参数的numpy.random.random()函数][numpy.random.random_ _ function with no input parameter]
40. [randomisation() Function to generate Random Vector][randomisation_ Function to generate Random Vector]
    
    [randomisation()函数生成随机向量][randomisation_ Function to generate Random Vector]
41. [randomisation\_matrix() Function to generate Random Matrix][randomisation_matrix_ Function to generate Random Matrix]
    
    [randomisation\_matrix()函数生成随机矩阵][randomisation_matrix_ Function to generate Random Matrix]
42. [Printing the power of vector/matrix elements using pow(x,a)][Printing the power of vector_matrix elements using pow_x_a]
    
    [使用pow(x，a)打印矢量/矩阵元素的幂][Printing the power of vector_matrix elements using pow_x_a]
43. [Printing sin value of vector/matrix elements using numpy.sin()][Printing sin value of vector_matrix elements using numpy.sin]
    
    [使用numpy.sin()打印向量/矩阵元素的sin值][Printing sin value of vector_matrix elements using numpy.sin]
44. [Printing hyperbolic tangent value of vector/matrix elements using numpy.tanh()][Printing hyperbolic tangent value of vector_matrix elements using numpy.tanh]
    
    [使用numpy.tanh()打印向量/矩阵元素的双曲正切值][Printing hyperbolic tangent value of vector_matrix elements using numpy.tanh]
45. [Printing Cosine value of vector/matrix (element wise operation)][Printing Cosine value of vector_matrix _element wise operation]
    
    [打印向量/矩阵的余弦值(明智的操作)][Printing Cosine value of vector_matrix _element wise operation]
46. [Printing logarithmic value of vector/matrix (element wise operation)][Printing logarithmic value of vector_matrix _element wise operation]
    
    [打印向量/矩阵的对数值(元素明智的操作)][Printing logarithmic value of vector_matrix _element wise operation]
47. [Printing exponential value of vector/matrix elements using numpy.exp()][Printing exponential value of vector_matrix elements using numpy.exp]
    
    [使用numpy.exp()打印矢量/矩阵元素的指数值][Printing exponential value of vector_matrix elements using numpy.exp]
48. [Print the identity matrix using numpy.eye() function][Print the identity matrix using numpy.eye_ function]
    
    [使用numpy.eye()函数打印身份矩阵][Print the identity matrix using numpy.eye_ function]
49. [Identity Matrix Property (I^k = I)][Identity Matrix Property _I_k _ I]
    
    [单位矩阵属性(I ^ k = I)][Identity Matrix Property _I_k _ I]
50. [Identity Matrix Property (AI = A)][Identity Matrix Property _AI _ A]
    
    [身份矩阵属性(AI = A)][Identity Matrix Property _AI _ A]
51. [Representation of a Linear Equation][]
    
    [线性方程的表示][Representation of a Linear Equation]
52. [Representation of a System of Linear Equation][]
    
    [线性方程组的表示][Representation of a System of Linear Equation]
53. [Transpose Matrix][]
    
    [转置矩阵][Transpose Matrix]
54. [Identity Matrix Transpose Property][]
    
    [单位矩阵转置属性][Identity Matrix Transpose Property]
55. [Symmetric Matrices][]
    
    [对称矩阵][Symmetric Matrices]
56. [Creating Symmetric Matrices][]
    
    [创建对称矩阵][Creating Symmetric Matrices]
57. [Sum of Symmetric Matrices][]
    
    [对称矩阵之和][Sum of Symmetric Matrices]
58. [Ones matrix using numpy.ones()][Ones matrix using numpy.ones]
    
    [使用numpy.ones()的人矩阵][Ones matrix using numpy.ones]
59. [Zeros Matrix using numpy.zeros()][Zeros Matrix using numpy.zeros]
    
    [使用numpy.zeros()的Zeros矩阵][Zeros Matrix using numpy.zeros]
60. [Determinant of a Matrix][]
    
    [矩阵的行列式][Determinant of a Matrix]
61. [Determinant of Identity Matrix][]
    
    [身份矩阵的行列式][Determinant of Identity Matrix]
62. [Determinant of a Transpose Matrix][]
    
    [转置矩阵的行列式][Determinant of a Transpose Matrix]
63. [Determinant of a Zeros and Ones matrices][]
    
    [零和一矩阵的行列式][Determinant of a Zeros and Ones matrices]
64. [Determinant of a non-square matrix][]
    
    [非平方矩阵的行列式][Determinant of a non-square matrix]
65. [Inverse of a Matrix][]
    
    [矩阵的逆][Inverse of a Matrix]
66. [Inverse of an Identity Matrix][]
    
    [单位矩阵的逆][Inverse of an Identity Matrix]
67. [Minimum value from a Matrix][]
    
    [矩阵的最小值][Minimum value from a Matrix]
68. [Maximum value from a Matrix][]
    
    [矩阵的最大值][Maximum value from a Matrix]
69. [Mean value from a Matrix][]
    
    [矩阵的平均值][Mean value from a Matrix]
70. [Product of a Matrix and its Inverse Property][]
    
    [矩阵的乘积及其逆性质][Product of a Matrix and its Inverse Property]
71. [Product of a Matrix and its Transpose Property][]
    
    [矩阵的乘积及其转置特性][Product of a Matrix and its Transpose Property]
72. [Comparing Maximum from Matrices][]
    
    [从矩阵比较最大值][Comparing Maximum from Matrices]
73. [Comparing Minimum from Matrices][]
    
    [从矩阵比较最小值][Comparing Minimum from Matrices]
74. [Norm of the Vector][]
    
    [向量的范数][Norm of the Vector]
75. [Outer Product of Vectors][]
    
    [向量的外积][Outer Product of Vectors]
76. [Outer Product Properties][]
    
    [外部产品属性][Outer Product Properties]
77. [Python | Application to School CPI Records (Linear Algebra)][Python _ Application to School CPI Records _Linear Algebra]
    
    [Python |][Python _ Application to School CPI Records _Linear Algebra] [申请学校CPI记录(线性代数)][Python _ Application to School CPI Records _Linear Algebra]

## 神经网络 **(**Neural Network**)** ##

1.  [Introduction to Simplest Neural Network][]
    
    [最简单的神经网络简介][Introduction to Simplest Neural Network]
2.  [Uni - Layer Neural Network][]
    
    [单层神经网络][Uni - Layer Neural Network]
3.  [Python | One Hidden Layer Simplest Neural Network][Python _ One Hidden Layer Simplest Neural Network]
    
    [Python |][Python _ One Hidden Layer Simplest Neural Network] [隐层最简单神经网络][Python _ One Hidden Layer Simplest Neural Network]

## 线性代数在机器学习中的应用 **(**Application of Linear Algebra in Machine Learning**)** ##

1.  [Hinge Loss for Single Point][]
    
    [单点铰链损耗][Hinge Loss for Single Point]
2.  [Function for Hinge Loss for Single Point][]
    
    [单点铰链损失功能][Function for Hinge Loss for Single Point]
3.  [Function for Hinge Loss for Multiple Points][]
    
    [多点铰链损失功能][Function for Hinge Loss for Multiple Points]
4.  [Binomial Process][]
    
    [二项式过程][Binomial Process]
5.  [Python | Binomial Experiment Simulation][Python _ Binomial Experiment Simulation]
    
    [Python |][Python _ Binomial Experiment Simulation] [二项式实验模拟][Python _ Binomial Experiment Simulation]
6.  [Euclidean Distance Example][]
    
    [欧氏距离示例][Euclidean Distance Example]

> 翻译自: [https://www.includehelp.com/python/linear-algebra.aspx][https_www.includehelp.com_python_linear-algebra.aspx]

线性代数 python

[Defining a Vector using list]: https://www.includehelp.com/python/defining-a-vector.aspx
[Defining Vector using Numpy]: https://www.includehelp.com/python/defining-vector-using-numpy.aspx
[Vector with User Defined Length]: https://www.includehelp.com/python/vector-with-user-defined-length.aspx
[Adding two vectors]: https://www.includehelp.com/python/adding-two-vectors.aspx
[Scalar Multiplication of Vector]: https://www.includehelp.com/python/scalar-multiplication-of-vector.aspx
[Scalar Multiplication of Vector using NumPy]: https://www.includehelp.com/python/scalar-multiplication-of-vector-using-numpy.aspx
[Scalar Multiplication Property 1]: https://www.includehelp.com/python/scalar-multiplication-property-1.aspx
[Scalar Multiplication Property 2]: https://www.includehelp.com/python/scalar-multiplication-property-2.aspx
[Adding Dimension to the Vector]: https://www.includehelp.com/python/adding-dimension-to-the-vector.aspx
[Calling ith dimensional Component of Vector]: https://www.includehelp.com/python/calling-ith-dimensional-component-of-vector.aspx
[Vector Magnitude using Function]: https://www.includehelp.com/python/vector-magnitude-using-function.aspx
[Dot Product of Vectors]: https://www.includehelp.com/python/dot-product-of-vectors.aspx
[Cosine Similarity between two vectors]: https://www.includehelp.com/python/cosine-similarity-between-two-vectors.aspx
[A Linear Function Vector]: https://www.includehelp.com/python/a-linear-function-vector.aspx
[Random Integer Vector]: https://www.includehelp.com/python/random-integer-vector.aspx
[Defining Matrix using Numpy]: https://www.includehelp.com/python/defining-matrix-using-numpy.aspx
[Creating a Matrix using Columns]: https://www.includehelp.com/python/creating-a-matrix-using-columns.aspx
[Creating a Matrix using Rows]: https://www.includehelp.com/python/creating-a-matrix-using-rows.aspx
[Calling Column of a Matrix]: https://www.includehelp.com/python/calling-column-of-a-matrix.aspx
[Calling Row of a Matrix]: https://www.includehelp.com/python/calling-row-of-a-matrix.aspx
[Matrix Addition]: https://www.includehelp.com/python/matrix-addition.aspx
[Row numbers in a Matrix]: https://www.includehelp.com/python/row-numbers-in-a-matrix.aspx
[Scalar Multiplication of Matrix]: https://www.includehelp.com/python/scalar-multiplication-of-matrix.aspx
[Shape of Matrix]: https://www.includehelp.com/python/shape-of-matrix.aspx
[i_j_ Element from a Matrix]: https://www.includehelp.com/python/i-j-element-from-a-matrix.aspx
[Calling Column of a Matrix using Function]: https://www.includehelp.com/python/calling-column-of-a-matrix-using-function.aspx
[Calling Row of a Matrix using Function]: https://www.includehelp.com/python/calling-row-of-a-matrix-using-function.aspx
[Checking Square Matrix]: https://www.includehelp.com/python/checking-square-matrix.aspx
[Python _ Vandermonde Matrix]: https://www.includehelp.com/python/vandermonde-matrix.aspx
[numpy.matmul_ _ for Matrix Multiplication]: https://www.includehelp.com/python/numpy-matmul-for-matrix-multiplication.aspx
[Python _ Constant Matrix]: https://www.includehelp.com/python/constant-matrix.aspx
[Python _ Range of a Matrix]: https://www.includehelp.com/python/range-of-a-matrix.aspx
[Python _ Rank of a Matrix]: https://www.includehelp.com/python/rank-of-a-matrix.aspx
[Python _ Trace of a Matrix]: https://www.includehelp.com/python/trace-of-a-matrix.aspx
[Python _ Sign and Natural Logarithm of Determinant of a Matrix]: https://www.includehelp.com/python/sign-and-natural-logarithm-of-determinant-of-a-matrix.aspx
[Python _ Diagonal of a Matrix]: https://www.includehelp.com/python/diagonal-of-a-matrix.aspx
[Python _ Lower Triangle of a Matrix]: https://www.includehelp.com/python/lower-triangle-of-a-matrix.aspx
[Python _ Upper Triangle of a Matrix]: https://www.includehelp.com/python/upper-triangle-of-a-matrix.aspx
[numpy.random.random_ _ function with no input parameter]: https://www.includehelp.com/python/numpy-random-random-function-with-no-input-parameter-linear-algebra-using-python.aspx
[randomisation_ Function to generate Random Vector]: https://www.includehelp.com/python/randomisation-function-to-generate-random-vector.aspx
[randomisation_matrix_ Function to generate Random Matrix]: https://www.includehelp.com/python/randomisation_matrix-function-to-generate-random-matrix.aspx
[Printing the power of vector_matrix elements using pow_x_a]: https://www.includehelp.com/python/printing-the-power-of-vector-matrix-elements-using-pow-x-a.aspx
[Printing sin value of vector_matrix elements using numpy.sin]: https://www.includehelp.com/python/printing-sin-value-of-vector-matrix-elements-using-numpy-sin.aspx
[Printing hyperbolic tangent value of vector_matrix elements using numpy.tanh]: https://www.includehelp.com/python/printing-hyperbolic-tangent-value-of-vector-matrix-elements-using-numpy-tanh.aspx
[Printing Cosine value of vector_matrix _element wise operation]: https://www.includehelp.com/python/printing-cosine-value-of-vector-matrix-element-wise-operation.aspx
[Printing logarithmic value of vector_matrix _element wise operation]: https://www.includehelp.com/python/printing-logarithmic-value-of-vector-matrix-element-wise-operation.aspx
[Printing exponential value of vector_matrix elements using numpy.exp]: https://www.includehelp.com/python/printing-exponential-value-of-vector-matrix-elements-using-numpy-exp.aspx
[Print the identity matrix using numpy.eye_ function]: https://www.includehelp.com/python/print-the-identity-matrix-using-numpy-eye-function.aspx
[Identity Matrix Property _I_k _ I]: https://www.includehelp.com/python/identity-matrix-property-i-k-i.aspx
[Identity Matrix Property _AI _ A]: https://www.includehelp.com/python/identity-matrix-property-ai-a.aspx
[Representation of a Linear Equation]: https://www.includehelp.com/python/representation-of-a-linear-equation.aspx
[Representation of a System of Linear Equation]: https://www.includehelp.com/python/representation-of-a-system-of-linear-equation.aspx
[Transpose Matrix]: https://www.includehelp.com/python/transpose-matrix.aspx
[Identity Matrix Transpose Property]: https://www.includehelp.com/python/identity-matrix-transpose-property.aspx
[Symmetric Matrices]: https://www.includehelp.com/python/symmetric-matrices.aspx
[Creating Symmetric Matrices]: https://www.includehelp.com/python/creating-symmetric-matrices.aspx
[Sum of Symmetric Matrices]: https://www.includehelp.com/python/sum-of-symmetric-matrices.aspx
[Ones matrix using numpy.ones]: https://www.includehelp.com/python/ones-matrix-using-numpy-ones.aspx
[Zeros Matrix using numpy.zeros]: https://www.includehelp.com/python/zeros-matrix-using-numpy-zeros.aspx
[Determinant of a Matrix]: https://www.includehelp.com/python/determinant-of-a-matrix.aspx
[Determinant of Identity Matrix]: https://www.includehelp.com/python/determinant-of-identity-matrix.aspx
[Determinant of a Transpose Matrix]: https://www.includehelp.com/python/determinant-of-a-transpose-matrix.aspx
[Determinant of a Zeros and Ones matrices]: https://www.includehelp.com/python/determinant-of-a-zeros-and-ones-matrices.aspx
[Determinant of a non-square matrix]: https://www.includehelp.com/python/determinant-of-a-non-square-matrix.aspx
[Inverse of a Matrix]: https://www.includehelp.com/python/inverse-of-a-matrix.aspx
[Inverse of an Identity Matrix]: https://www.includehelp.com/python/inverse-of-an-identity-matrix.aspx
[Minimum value from a Matrix]: https://www.includehelp.com/python/minimum-value-from-a-matrix.aspx
[Maximum value from a Matrix]: https://www.includehelp.com/python/maximum-value-from-a-matrix.aspx
[Mean value from a Matrix]: https://www.includehelp.com/python/mean-value-from-a-matrix.aspx
[Product of a Matrix and its Inverse Property]: https://www.includehelp.com/python/product-of-a-matrix-and-its-inverse-property.aspx
[Product of a Matrix and its Transpose Property]: https://www.includehelp.com/python/product-of-a-matrix-and-its-transpose-property.aspx
[Comparing Maximum from Matrices]: https://www.includehelp.com/python/comparing-maximum-from-matrices.aspx
[Comparing Minimum from Matrices]: https://www.includehelp.com/python/comparing-minimum-from-matrices.aspx
[Norm of the Vector]: https://www.includehelp.com/python/norm-of-the-vector.aspx
[Outer Product of Vectors]: https://www.includehelp.com/python/outer-product-of-vectors.aspx
[Outer Product Properties]: https://www.includehelp.com/python/outer-product-properties.aspx
[Python _ Application to School CPI Records _Linear Algebra]: https://www.includehelp.com/python/application-to-school-cpi-records-linear-algebra.aspx
[Introduction to Simplest Neural Network]: https://www.includehelp.com/python/introduction-to-simplest-neural-network.aspx
[Uni - Layer Neural Network]: https://www.includehelp.com/python/uni-layer-neural-network.aspx
[Python _ One Hidden Layer Simplest Neural Network]: https://www.includehelp.com/python/one-hidden-layer-simplest-neural-network.aspx
[Hinge Loss for Single Point]: https://www.includehelp.com/python/hinge-loss-for-single-point.aspx
[Function for Hinge Loss for Single Point]: https://www.includehelp.com/python/function-for-hinge-loss-for-single-point.aspx
[Function for Hinge Loss for Multiple Points]: https://www.includehelp.com/python/function-for-hinge-loss-for-multiple-points.aspx
[Binomial Process]: https://www.includehelp.com/python/binomial-process.aspx
[Python _ Binomial Experiment Simulation]: https://www.includehelp.com/python/binomial-experiment-simulation.aspx
[Euclidean Distance Example]: https://www.includehelp.com/python/euclidean-distance-example.aspx
[https_www.includehelp.com_python_linear-algebra.aspx]: https://www.includehelp.com/python/linear-algebra.aspx