Data update

Task/Conjugate-transpose/R/conjugate-transpose.r

@@ -0,0 +1,69 @@
+conjugate_transpose<- function(M){
+  t(Conj(M))}
+
+is_hermitian <- function(M,eps=10**-10){
+  all(abs(M-conjugate_transpose(M))<eps)
+}
+
+is_normal <-function(M,eps=10**-10){
+  conjugate <- conjugate_transpose(M)
+ all(abs(M%*%conjugate- conjugate%*%M)<eps)
+}
+
+is_unitary  <-function(M,eps=10**-10){
+ all(abs(M%*% conjugate_transpose(M)-diag(nrow(M)))<eps)
+}
+
+M1 = matrix(c(3+0i,2-1i,
+              2+1i,1+0i),nrow=2)
+cat("M1")
+cat("\n")
+print(M1)
+cat("\n")
+Conj_M1 = conjugate_transpose(M1)
+cat("Conjugate transpose of M1")
+cat("\n")
+print(Conj_M1)
+cat(paste0("Hermitian ? ", is_hermitian(M1)))
+cat("\n")
+cat(paste0("Normal ? ", is_normal(M1)))
+cat("\n")
+cat(paste0("Unitary ? ", is_unitary(M1)))
+
+
+M2 = matrix(c(1+0i,0+0i,1+0i,
+              1+0i,1+0i,0+0i,
+              0+0i,1+0i,1+0i),nrow=3)
+cat("\n")
+cat("M2")
+cat("\n")
+print(M2)
+cat("\n")
+Conj_M2 = conjugate_transpose(M2)
+cat("Conjugate transpose of M2")
+cat("\n")
+print(Conj_M2)
+cat(paste0("Hermitian ? ", is_hermitian(M2)))
+cat("\n")
+cat(paste0("Normal ? ", is_normal(M2)))
+cat("\n")
+cat(paste0("Unitary ? ", is_unitary(M2)))
+
+
+M3 = matrix(c(sqrt(2)/2+0i,0-(sqrt(2)/2)*1i,0+0i,
+              sqrt(2)/2+0i,0+(sqrt(2)/2)*1i,0+0i,
+              0+0i,0+0i,0+1i),ncol=3)
+cat("\n")
+cat("M3")
+cat("\n")
+print(M3)
+cat("\n")
+Conj_M3 = conjugate_transpose(M3)
+cat("Conjugate transpose of M3")
+cat("\n")
+print(Conj_M3)
+cat(paste0("Hermitian ? ", is_hermitian(M3)))
+cat("\n")
+cat(paste0("Normal ? ", is_normal(M3)))
+cat("\n")
+cat(paste0("Unitary ? ", is_unitary(M3)))