library(matrixcalc) library(Matrix) # Decomposição LU A<-matrix(c(2,1,0,2,2,1,4,1,2),nrow=3,byrow=T) A E1<-matrix(c(1,0,0,-1,1,0,-2,0,1),nrow=3,byrow=T) E1 %*% A E2<-matrix(c(1,0,0,0,1,0,0,1,1),nrow=3,byrow=T) E2 %*% E1 %*% A L <- matrix(c(1,0,0,1,1,0,2,-1,1),nrow=3,byrow=T) U <- matrix(c(2,1,0,0,1,1,0,0,3),nrow=3,byrow=T) L %*% U L U lu.decomposition(A) # Decomposição LDL' A<-matrix(c(2,2,4,2,1,1,4,1,2),nrow=3,byrow=T) A #A é simétrica? is.symmetric.matrix(A) E1<-matrix(c(1,0,0,-1,1,0,-2,0,1),nrow=3,byrow=T) E1 E1 %*% A E2 <- matrix(c(1,0,0,0,1,0,0,-3,1),nrow=3,byrow=T) E2 E2 %*% E1 %*% A L <- matrix(c(1,0,0,1,1,0,2,3,1),nrow=3,byrow=T) L U <- t(L) U D <-diag(c(2,-1,3)) L %*% D %*% U # Decomposição de Cholesky A<-matrix(c(4,4,8,4,5,11,8,11,34),nrow=3,byrow=T) A det(A) #A é simétrica? is.symmetric.matrix(A) # A é positiva definida? rankMatrix(A) E1<-matrix(c(1,0,0,-1,1,0,-2,0,1),nrow=3,byrow=T) E1 E1 %*% A E2 <- matrix(c(1,0,0,0,1,0,0,-3,1),nrow=3,byrow=T) E2 E2 %*% E1 %*% A L <- matrix(c(1,0,0,1,1,0,2,3,1),nrow=3,byrow=T) L U <- t(L) U D <-diag(c(4,1,9)) L %*% D %*% U C<- sqrt(D) %*% U chol(A, pivot=F)