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| author | Prashant S | 2019-10-04 12:27:32 +0530 |
|---|---|---|
| committer | GitHub | 2019-10-04 12:27:32 +0530 |
| commit | ac2986488a9731cff5cbb517d8f0ef98e2561d64 (patch) | |
| tree | 7bb3f64824627ef179d5f341266a664fd0b69011 /Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4 | |
| parent | cbb2770fb2f88246175add29623103a56ba338b8 (diff) | |
| parent | b3f3a8ecd454359a2e992161844f2fb599f8238a (diff) | |
| download | R_TBC_Uploads-master.tar.gz R_TBC_Uploads-master.tar.bz2 R_TBC_Uploads-master.zip | |
Added R TBC
Diffstat (limited to 'Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4')
| -rw-r--r-- | Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4/Ex6.1_4.r | 81 |
1 files changed, 81 insertions, 0 deletions
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4/Ex6.1_4.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4/Ex6.1_4.r new file mode 100644 index 00000000..6d8b139e --- /dev/null +++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH6/EX6.1.4/Ex6.1_4.r @@ -0,0 +1,81 @@ +# Packages used : pracma
+# To install pracma,type following in command line while connected to internet
+# install.packages("pracma")
+# package can be included by command " library(pracma) "
+# for more information about pracma visit https://cran.r-project.org/web/packages/pracma/index.html
+
+# Example : 4 Chapter : 6.1 Page No: 287
+# Eigen values and eigen vectors of Singualar matrix
+
+library(pracma)
+nullspacebasis <- function(A){
+ R<-rref(A)
+ m<-nrow(A)
+ n<-ncol(A)
+ pivotcol<-c() #vector to store the column numbers of pivot columns
+ freecol<-c() #vector to store the column numbers of free columns
+ i<-1
+ j<-1
+
+ # to find which columns are pivot and which are free
+ while(i<=m & j<=n){
+ if(R[i,j]==1){
+ pivotcol<-c(pivotcol,j)
+ i<-i+1
+ j<-j+1
+ }
+ else{
+ j<-j+1
+ }
+ }
+ y<-length(pivotcol)
+ freecol<-c(1:n)
+ freecol<-freecol[!freecol%in%pivotcol]
+ x<-length(freecol)
+ N<-c()
+ #find the basis for null space based on Row reduced echelon form of given matrix
+ if(y==n){
+ return(N)
+ }
+ for(i in 1:x){
+ temp<-c(1:n)
+ for(j in 1:x){
+ temp[freecol[j]]<-0
+ }
+ temp[freecol[i]]<-1
+ temp[freecol[i]]
+ for(j in 1:y){
+ temp[pivotcol[j]]<-R[j,freecol[i]]*-1
+ }
+ N<-c(N,temp)
+ }
+ N<-matrix(N,nrow=n,ncol=x)
+ #Basis for the nullspace of given matrix
+ return(N)
+}
+A<-matrix(c(1,2,2,4),ncol=2)
+sol<-eigen(A)
+print(sol)
+lambda<-sol$values
+print("The eigen values of the matrix are")
+print(lambda)
+I<-matrix(c(1,0,0,1),ncol=2)
+E1<-A-lambda[1]*I
+E1
+rref(E1)
+x1<-nullspacebasis(E1)
+E2<-A-lambda[2]*I
+rref(E2)
+x2<-nullspacebasis(E2)
+print("The eigen vectors of the matrix in normalized form are")
+print(x1)
+print(x2)
+#to get eigen vectors in the textbook multiply normalised vectors by scalars
+x1<-2*x1
+x2<--1*x2
+print("The eigen vectors of the matrix are ")
+print(x2)
+print(x1)
+#The answer may slightly vary due to rounding off values
+#The answers provided in the text book may vary because of the computation process
+#Both answers are correct , here it is taken -Ax+b=0 , In the text book it is considered as Ax-b=0
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