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14-09-2020GRam
# Processo de ortogonalização de Gram-Schmdit pe<-function(u,v){ # Dados os vetores u e v, somo o produto de cada coordenada de u com a respectiva cooordenada de v. n=length(u) p=u[1]*v[1] for ( i in 2:n){p=p+u[i]*v[i]} p } mod<-function(u){sqrt(pe(u,u))} # módulo de u proj<-function(u,v){pe(u,v)*v} # Projeção de u sobre v (ortogonal), com norma de v igual 1 pe(c(1,2,3),c(1,1,1)) mod(c(1,1,1)) proj(c(1,2,3),c(1,1,1)) GramS<-function(A){ # Ortogonliza as colunas de A n=length(A[1,]) Q=0*A Q[,1]=A[,1]/mod(A[,1]) for (i in 2:n){ p=A[,i] for (j in 1:(i-1)){ p=p-proj(A[,i],Q[,j]) } Q[,i]=p/mod(p) } Q } A=matrix(c ( 4, 6, 7, 1, 3, 4, 8, 5, 6), 3,3,byrow=TRUE);A Q=GramS(A); Q; t(Q)%*%Q # Teste de ortogonalização
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