Vectors and Matrices in Python Solutions
Vectors and Matrices in Python Solutions Exercise 1 : Vectors in $\mathbb{R}^7$ Consider the following vectors: $$ u = (0.5, 0.4, 0.4, 0.5, 0.1, 0.4, 0.1), \quad v = (-1, -2, 1, -2, 3, 1, -5) $$Using Python and NumPy: Check whether $u$ and $v$ are unit vectors. Compute the dot product of $u$ and $v$. Determine if $u$ and $v$ are orthogonal. import numpy as np u = np.array([0.5, 0.4, 0.4, 0.5, 0.1, 0.4, 0.1]) v = np.array([-1, -2, 1, -2, 3, 1, -5]) # 1. Check if u and v are unit vectors norm_u = np.linalg.norm(u) norm_v = np.linalg.norm(v) print(norm_u, norm_v) # 2. Dot product dot_uv = np.dot(u, v) print(dot_uv) # 3. Orthogonality print(np.isclose(dot_uv, 0)) Exercise 2 : Norms and Orthogonality Consider the following vectors in $\mathbb{R}^9$: ...