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Book4_Ch03_Python_Codes/Bk4_Ch3_01.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_01.py
+
+import numpy as np
+
+# 2d matrix
+A_matrix = np.matrix([[2,4],
+                      [6,8]])
+print(A_matrix.shape)
+print(type(A_matrix))
+
+# 1d array
+A_1d = np.array([2,4])
+print(A_1d.shape)
+print(type(A_1d))
+
+# 2d array
+A_2d = np.array([[2,4],
+                 [6,8]])
+print(A_2d.shape)
+print(type(A_2d))
+
+# 3d array
+A1 = [[2,4],
+      [6,8]]
+
+A2 = [[1,3],
+      [5,7]]
+
+A3 = [[1,0],
+      [0,1]]
+A_3d = np.array([A1,A2,A3])
+print(A_3d.shape)
+print(type(A_3d))

Book4_Ch03_Python_Codes/Bk4_Ch3_02.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_02.py
+
+import numpy as np
+
+A = np.matrix([[1,2,3],
+              [4,5,6],
+              [7,8,9]])
+
+# extract diagonal elements
+a = np.diag(A)
+
+# construct a diagonal matrix
+A_diag = np.diag(a)

Book4_Ch03_Python_Codes/Bk4_Ch3_03.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_03.py
+
+import numpy as np
+
+# define matrix
+A = np.matrix([[1, 2], [3, 4]])
+B = np.matrix([[2, 6], [4, 8]])
+
+# matrix addition
+A_plus_B = np.add(A,B)
+A_plus_B_2 = A + B
+
+
+# matrix subtraction
+A_minus_B = np.subtract(A,B)
+A_minus_B_2 = A - B

Book4_Ch03_Python_Codes/Bk4_Ch3_04.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_04.py
+
+import numpy as np
+
+k = 2
+X = [[1,2],
+     [3,4]]
+
+# scalar multiplication
+k_times_X = np.dot(k,X)
+k_times_X_2 = k*np.matrix(X)

Book4_Ch03_Python_Codes/Bk4_Ch3_05.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_05.py
+
+import numpy as np
+
+# define matrix
+A = np.matrix([[1, 2], 
+               [3, 4],
+               [5, 6]])
+
+# scaler
+k = 2;
+
+# column vector c
+c = np.array([[3],
+              [2],
+              [1]])
+
+# row vector r
+r = np.array([[2,1]])
+
+# broadcasting principles
+
+# matrix A plus scalar k
+A_plus_k = A + k
+
+# matrix A plus column vector c
+A_plus_a = A + c
+
+# matrix A plus row vector r
+A_plus_r = A + r
+
+# column vector c plus row vector r
+c_plus_r = c + r

Book4_Ch03_Python_Codes/Bk4_Ch3_06.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_06.py
+
+import numpy as np
+
+A = np.array([[1, 2],
+              [3, 4]])
+
+B = np.array([[2, 4],
+              [1, 3]])
+
+# matrix multiplication
+A_times_B = np.matmul(A, B)
+A_times_B_2 = A@B

Book4_Ch03_Python_Codes/Bk4_Ch3_07.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_07.py
+
+import numpy as np
+
+A = np.array([[1, 2]])
+
+B = np.array([[5, 6], 
+              [8, 9]])
+
+print(A*B)
+
+A = np.array([[1, 2]])
+
+B = np.matrix([[5, 6], 
+              [8, 9]])
+
+print(A*B)
+
+A = np.matrix([[1, 2]])
+
+B = np.matrix([[5, 6], 
+              [8, 9]])
+
+print(A*B)

Book4_Ch03_Python_Codes/Bk4_Ch3_08.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_08.py
+
+from numpy.linalg import matrix_power as pw
+A = np.array([[1., 2.], 
+              [3., 4.]])
+
+# matrix inverse
+A_3 = pw(A,3)
+A_3_v3 = A@A@A
+
+# piecewise power
+A_3_piecewise = A**3

Book4_Ch03_Python_Codes/Bk4_Ch3_09.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_09.py
+
+import numpy as np
+
+A = np.matrix([[1,3],
+               [2,4]])
+
+print(A**2)
+
+B = np.array([[1,3],
+              [2,4]])
+
+print(B**2)

Book4_Ch03_Python_Codes/Bk4_Ch3_10.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_10.py
+
+import numpy as np
+
+A = np.array([[1, 2],
+              [3, 4],
+              [5, 6]])
+
+# matrix transpose
+A_T = A.transpose()
+A_T_2 = A.T

Book4_Ch03_Python_Codes/Bk4_Ch3_11.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_11.py
+
+from numpy.linalg import inv
+A = np.array([[1., 2.], 
+              [3., 4.]])
+
+# matrix inverse
+A_inverse = inv(A)
+A_times_A_inv = A@A_inverse

Book4_Ch03_Python_Codes/Bk4_Ch3_12.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_12.py
+
+import numpy as np
+
+A = np.matrix([[1, 2], 
+               [3, 4]])
+
+print(A.I)
+
+B = np.array([[1, 2], 
+              [3, 4]])
+
+print(B.I)

Book4_Ch03_Python_Codes/Bk4_Ch3_13.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_13.py
+
+import numpy as np
+A = np.array([[1, -1, 0], 
+              [3,  2, 4],
+              [-2, 0, 3]])
+
+# calculate trace of A
+tr_A = np.trace(A)

Book4_Ch03_Python_Codes/Bk4_Ch3_14.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_14.py
+
+import numpy as np
+
+A = np.array([[1,2],
+              [3,4]])
+
+B = np.array([[5,6],
+              [7,8]])
+
+# Hadamard product
+A_times_B_piecewise = np.multiply(A,B)
+A_times_B_piecewise_V2 = A*B

Book4_Ch03_Python_Codes/Bk4_Ch3_15.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch3_15.py
+
+import numpy as np
+A = np.array([[3, 1], 
+              [2, 4]])
+
+# calculate determinant of A
+det_A = np.linalg.det(A)