Atividades 6:

1. Arquivo N01.py: Representa em Python as matrices como Python lists of lists: \(\underline{\underline{\textbf{A}}}_0= \left(\begin{array}{cccc} 1& 1& 1& 1\\1&-1& 1&-1\\1& 1&-1&-1\\-1& 1& 1&-1\\\end{array}\right),\) \(\underline{\underline{\textbf{A}}}_1= \left(\begin{array}{cccc}1& 2& 4& 8\\1&-1& 1&-1\\1&-2& 4&-8\\1& 1& 1& 1\\\end{array}\right),\) \(\underline{\underline{\textbf{A}}}_2=\left(\begin{array}{cccc}1& 1& 1& 1\\1&-1& 1&-1\\1& 2& 4& 8\\1& 3& 9&27\\\end{array}\right),\) \(\underline{\underline{\textbf{A}}}_3=\left(\begin{array}{cccc}1& 1& 1& 1\\1& 2& 4& 8\\1& 3& 9&27\\1& 4&16&64\\\end{array}\right),\)

   Python Listing: N01.py. from Matrix import * #Lista de matrices A=[ [ [ 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,], ], Matrix_Vandermonte([ 2.0,-1.0,-2.0, 1.0 ]), Matrix_Vandermonte([ 1.0,-1.0, 2.0, 3.0 ]), Matrix_Vandermonte([ 1.0, 2.0, 3.0, 4.0 ]), ]

2. Arquivo N02.py: Usando um laço duplo, calcule as matrices: \(\underline{\underline{\textbf{A}}}_i +\underline{\underline{\textbf{A}}}_j, ~ i,j \in \{0,1,2,3\}.\)

   Python Listing: N02.py. from Matrix import * from N01 import * for i in range( len(A) ): for j in range( len(A) ): print i,j,":" B=Matrices_Add(A[i],A[j]) Matrix_Print(A[i]) print "+" Matrix_Print(A[j]) print "=" Matrix_Print(B)

3. Arquivo N03.py: Usando um laço duplo, calcule os vetores: \(\underline{\underline{\textbf{A}}}_i -\underline{\underline{\textbf{A}}}_j, ~ i,j \in \{0,1,2,3\}.\)
4. Arquivo N04.py: Calcular os produtos: \(\underline{\underline{\textbf{A}}}_i ~\underline{\underline{\textbf{A}}}_j\) e \(\underline{\underline{\textbf{A}}}_j ~\underline{\underline{\textbf{A}}}_i, ~ i,j \in \{0,1,2,3\}.\)
5. Arquivo N05.py: Calcular a comutação das matrices \(\underline{\underline{\textbf{A}}}_i ;] e [; \underline{\underline{\textbf{A}}}_j\) \(\underline{\underline{\textbf{D}}}_{ij}=\underline{\underline{\textbf{A}}}_i~\underline{\underline{\textbf{A}}}_j-\underline{\underline{\textbf{A}}}_j~\underline{\underline{\textbf{A}}}_i,~ i,j \in \{0,1,2,3\}.\)