Atividades 5:

1. Arquivo N01.py: Representa em Python os vetores como Python lists: \(\underline{\textbf{v}}_0= \left(\begin{array}{c} 1\\1\\1\\1 \end{array}\right) \quad \underline{\textbf{v}}_1= \left(\begin{array}{c} 1\\-1\\1\\-1 \end{array}\right), \quad \underline{\textbf{v}}_2= \left(\begin{array}{c} 1\\1\\-1\\-1 \end{array}\right), \quad \underline{\textbf{v}}_3= \left(\begin{array}{c} -1\\1\\1\\-1 \end{array}\right), \)

   Python Listing: N01.py. #Matrix with Vectors in rows v=[ [ 1.0, 1.0, 1.0, 1.0,], [ 1.0,-1.0, 1.0,-1.0,], [ 1.0, 1.0,-1.0,-1.0,], [-1.0, 1.0, 1.0,-1.0,], ]

2. Arquivo N02.py: Usando um laço duplo, calcule os vetores: \(\underline{\textbf{v}}_i +\underline{\textbf{v}}_j, \quad i,j \in \{0,1,2,3\}.\)

   Python Listing: N02.py. from Vector import * from N01 import * for i in range( len(v) ): for j in range( len(v) ): w=Vectors_Add(v[i],v[j]) print i,j,v[i],'+',v[j],'=',w

   0 0 [1.0, 1.0, 1.0, 1.0] + [1.0, 1.0, 1.0, 1.0] = [2.0, 2.0, 2.0, 2.0] 0 1 [1.0, 1.0, 1.0, 1.0] + [1.0, -1.0, 1.0, -1.0] = [2.0, 0.0, 2.0, 0.0] 0 2 [1.0, 1.0, 1.0, 1.0] + [1.0, 1.0, -1.0, -1.0] = [2.0, 2.0, 0.0, 0.0] 0 3 [1.0, 1.0, 1.0, 1.0] + [-1.0, 1.0, 1.0, -1.0] = [0.0, 2.0, 2.0, 0.0] 1 0 [1.0, -1.0, 1.0, -1.0] + [1.0, 1.0, 1.0, 1.0] = [2.0, 0.0, 2.0, 0.0] 1 1 [1.0, -1.0, 1.0, -1.0] + [1.0, -1.0, 1.0, -1.0] = [2.0, -2.0, 2.0, -2.0] 1 2 [1.0, -1.0, 1.0, -1.0] + [1.0, 1.0, -1.0, -1.0] = [2.0, 0.0, 0.0, -2.0] 1 3 [1.0, -1.0, 1.0, -1.0] + [-1.0, 1.0, 1.0, -1.0] = [0.0, 0.0, 2.0, -2.0] 2 0 [1.0, 1.0, -1.0, -1.0] + [1.0, 1.0, 1.0, 1.0] = [2.0, 2.0, 0.0, 0.0] 2 1 [1.0, 1.0, -1.0, -1.0] + [1.0, -1.0, 1.0, -1.0] = [2.0, 0.0, 0.0, -2.0] 2 2 [1.0, 1.0, -1.0, -1.0] + [1.0, 1.0, -1.0, -1.0] = [2.0, 2.0, -2.0, -2.0] 2 3 [1.0, 1.0, -1.0, -1.0] + [-1.0, 1.0, 1.0, -1.0] = [0.0, 2.0, 0.0, -2.0] 3 0 [-1.0, 1.0, 1.0, -1.0] + [1.0, 1.0, 1.0, 1.0] = [0.0, 2.0, 2.0, 0.0] 3 1 [-1.0, 1.0, 1.0, -1.0] + [1.0, -1.0, 1.0, -1.0] = [0.0, 0.0, 2.0, -2.0] 3 2 [-1.0, 1.0, 1.0, -1.0] + [1.0, 1.0, -1.0, -1.0] = [0.0, 2.0, 0.0, -2.0] 3 3 [-1.0, 1.0, 1.0, -1.0] + [-1.0, 1.0, 1.0, -1.0] = [-2.0, 2.0, 2.0, -2.0] Output from: /usr/bin/python N02.py

3. Arquivo N03.py: Usando um laço duplo, calcule os vetores: \(\underline{\textbf{v}}_i -\underline{\textbf{v}}_j, \quad i,j \in \{0,1,2,3\}.\)
4. Arquivo N04.py: Calcular os produtos escalarares: \(\underline{\textbf{v}}_i \cdot \underline{\textbf{v}}_j, \quad i,j \in \{0,1,2,3\}.\)
5. Arquivo N05.py: Calcular as projeções de \(\underline{\textbf{v}}_i\) em \(\underline{\textbf{v}}_j,\) \(i,j \in \{0,1,2,3\}.\)