Merge pull request #1 from prashantsinalkar/masterHEADmaster

Added R TBC

9 files changed, 112 insertions, 0 deletions

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX1.3/Ex5_1_3.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX1.3/Ex5_1_3.R
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+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX1.3/Ex5_1_3.R
@@ -0,0 +1,12 @@
+#Example 1.3,chapter 5,Section II. Similarity,page 390

+#package used matlib v0.9.1

+#Github reposiory of matlib :https://github.com/friendly/matlib

+

+#installation and loading library

+#install.packages("matlib")

+library("matlib")

+P <- matrix(c(2,1,1,1),ncol = 2)

+T <- matrix(c(2,1,-3,-1),ncol = 2)

+#finding similar matrix of T

+T1 <- P %*% T %*% Inverse(P)

+T1

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.10/Ex5_2_10.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.10/Ex5_2_10.R
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--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.10/Ex5_2_10.R
@@ -0,0 +1,16 @@
+#Example 2.10,chapter 5,scetion III.2,page 414

+#package used matlib v0.9.1

+#Github reposiory of matlib :https://github.com/friendly/matlib

+

+#installation and loading library

+#install.packages("matlib")

+library("matlib")

+N <- matrix(c(0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0),ncol=4)

+P <- matrix(c(1,0,1,0,0,2,1,0,1,1,1,0,0,0,0,1),ncol = 4)

+A <- P %*% N %*% Inverse(P)

+A

+#The new matrix,A is nilpotent; its fourth power is the zero matrix.

+x <- P %*% N^4 %*% Inverse(P) 

+#since (PNP^-1)^4 = P * N^4 *P^-1

+y <- det(x)

+all.equal(y,0)

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.17/Ex5_2_17.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.17/Ex5_2_17.R
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index 00000000..e6436638
--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.17/Ex5_2_17.R
@@ -0,0 +1,21 @@
+#Example 2.17,chapter 5,scetion III.2,page 419

+#package used matlib v0.9.1

+#Github reposiory of matlib :https://github.com/friendly/matlib

+

+#installation and loading library

+#install.packages("matlib")

+library("matlib")

+M <- matrix(c(1,1,-1,-1),ncol = 2)

+#finding nilpotent index

+A <- matrix(c(0,0,0,0),ncol = 2)

+count <- 1

+Y <- M

+repeat{

+  Y <- Y %*% M

+  if (all.equal(Y,A)){

+    print(count+1)

+    break()

+  }

+ count= count+1

+}

+

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.18/Ex5_2_18.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.18/Ex5_2_18.R
new file mode 100644
index 00000000..960e5899
--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.18/Ex5_2_18.R
@@ -0,0 +1,20 @@
+#Example 2.18,chapter 5,scetion III.2,page 420

+#package used matlib v0.9.1

+#Github reposiory of matlib :https://github.com/friendly/matlib

+

+#installation and loading library

+#install.packages("matlib")

+library("matlib")

+M <- matrix(c(0,1,-1,0,1,0,0,1,1,0,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1),ncol = 5)

+#finding nilpotent index

+A <- matrix(c(0),ncol = 5,nrow = 5)

+count <- 1

+Y <- M

+repeat{

+  Y <- Y %*% M

+  if (all.equal(Y,A)== TRUE){

+    print(count+1)

+    break()

+  }

+  count=count+1

+}

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2.2/Ex5_2_2_2.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2.2/Ex5_2_2_2.R
new file mode 100644
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--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2.2/Ex5_2_2_2.R
@@ -0,0 +1,7 @@
+#Example 2.2,chapter 5,section II.2 Diagonalizability,page 393

+#matrix: T is diagonalizable if there is a nonsingular P such that PTP-1 is diagonal.

+T <- matrix(c(4,1,-2,1),ncol = 2)

+P <- matrix(c(-1,1,2,-1),ncol = 2)

+#checking whether diagonizable

+P %*% T %*% Inverse(P) # diagonal matrix

+# so matrix P is diagonizable
\ No newline at end of file
diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2/Ex5_2_2.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2/Ex5_2_2.R
new file mode 100644
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--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.2/Ex5_2_2.R
@@ -0,0 +1,12 @@
+#Example 2.2,chapter 5,Section I. Complex Vector Spaces,page 387

+a <- complex(real = 1,imaginary = 1)

+b <- complex(real = 0,imaginary = 1)

+c <- complex(real = 2,imaginary = -0)

+d <- complex(real = -2,imaginary = 3)

+e <- complex(real = 1,imaginary = 0)

+f <- complex(real = 0,imaginary = 3)

+g <- complex(real = 1,imaginary = -0)

+h <- complex(real = 0,imaginary = -1)

+A <- matrix(c(a,b,c,d),ncol = 2)

+B <- matrix(c(e,f,g,h),ncol = 2)

+A %*% B

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.4/Ex5_2_4.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.4/Ex5_2_4.R
new file mode 100644
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--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX2.4/Ex5_2_4.R
@@ -0,0 +1,15 @@
+#Example 2.4,chapter 5,section IV.2,page 432

+#package used pracma v1.9.9

+#installing and loading library

+#install.packages("pracma")

+library("pracma")

+T <- matrix(c(2,1,-1,4),ncol=2)

+a <- eigen(T)

+a$values

+#so T has only the single eigenvalue 3.

+I <- matrix(c(1,0,0,1),ncol = 2)

+T-(3*I)

+# so for this,the only eigenvalue is 0 and T -3I is nilpotent.

+#to ease this computation we find nulspaces

+x <- nullspace(T)

+x

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.19/Ex5_3_19.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.19/Ex5_3_19.R
new file mode 100644
index 00000000..6b619a24
--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.19/Ex5_3_19.R
@@ -0,0 +1,4 @@
+#Example3.19,chapter 5,section II.3 Eigenvalues and Eigenvectors,page 404

+T <- matrix(c(2,0,-4,-2,1,8,2,1,3),ncol = 3)

+a <- eigen(T)

+a$values

diff --git a/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.6/Ex5_3_6.R b/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.6/Ex5_3_6.R
new file mode 100644
index 00000000..9bf70023
--- /dev/null
+++ b/Linear_Algebra_by_Jim_Hefferon/CH5/EX3.6/Ex5_3_6.R
@@ -0,0 +1,5 @@
+#Example3.6,chapter 5,section II.3 Eigenvalues and Eigenvectors,page 398

+T <- matrix(c(2,0,0,0),ncol = 2)

+a <-eigen(T)

+a$values

+a$vectors