Merge pull request #1 from prashantsinalkar/masterHEADmaster

Added R TBC

5 files changed, 68 insertions, 0 deletions

diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.1/Ex7.3_1.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.1/Ex7.3_1.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.1/Ex7.3_1.r
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+# Example : 1   Chapter : 7.3     Page No: 400
+# Diagonaliazation of matrix
+A<-matrix(c(0.5,-0.5,-0.5,0.5),ncol=2)
+ev<-eigen(A)$values
+D<-matrix(c(ev[1],0,0,ev[2]),ncol=2)
+print("The diagonialized matrix")
+print(D)
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diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.2/Ex7.3_2.r
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+# Example : 2   Chapter : 7.3     Page No: 401

+# Similar Projection Matrices

+A<-matrix(c(0.5,-0.5,-0.5,0.5),ncol=2)

+Aev<-eigen(A)$values

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

+W1<-solve(W)

+B<-W1%*%A%*%W

+print("Matrix B = W-1 * A * W")

+print(B)

+Bev<-eigen(B)$values

+print("A and B are similar matrices")

+print(Aev)

+print(Bev)
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diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.3/Ex7.3_3.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.3/Ex7.3_3.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.3/Ex7.3_3.r
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+# Example : 3   Chapter : 7.3     Page No: 402
+# Polar Decomposition
+A<-matrix(c(2,-1,2,1),ncol=2)
+Q<-round(svd(A)$u)%*%t(svd(A)$v)
+H<-t(Q)%*%A
+print("Polar Decomposition A=QH")
+print("Q is ")
+print(Q)
+print("H is ")
+print(H)
+#The  answer may slightly vary due to  rounding off values
+#The answers provided in the text book may vary because of the computation method followed.
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.4/Ex7.3_4.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.4/Ex7.3_4.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.4/Ex7.3_4.r
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+# Example : 4   Chapter : 7.3     Page No: 404
+# Pseduoinverse of matrix
+A<-matrix(c(2,1,2,1),ncol=2)
+V<-svd(A)$v
+UT<-t(svd(A)$u)
+d<-svd(A)$d
+sigma1<-matrix(c(1/d[1],0,0,0),ncol=2)
+A1<-V%*%sigma1%*%UT
+print("The Pseduo inverse of the given matrix")
+print(A1)
+#The  answer may slightly vary due to  rounding off values
+#The answers provided in the text book may vary because of the computation method followed.
diff --git a/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.a/Ex7_7.3A.r b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.a/Ex7_7.3A.r
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+++ b/Introduction_To_Linear_Algebra_by_Gilbert_Strang/CH7/EX7.3.a/Ex7_7.3A.r
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+# Example : 7.3A   Chapter : 7.3     Page No: 405

+# leftinverse,rightinverse,Pseduoinverse of given matrices

+A1<-matrix(c(2,2),ncol=1)

+A2<-matrix(c(2,2),ncol=2)

+A3<-matrix(c(2,2,2,2),ncol=2)

+A1T<-t(A1)

+A2T<-t(A2)

+A1inv<-solve(A1T%*%A1)%*%A1T

+print("Left inverse of A1")

+print(A1inv)

+print(A1inv%*%A1)

+A2inv<-A2T%*%solve(A2%*%A2T)

+print("right inverse of A2")

+print(A2inv)

+print(A2%*%A2inv)

+

+#The answers given in the text book is wrong it is 1/8 ..  not 1/sqrt(8)

+V1<-svd(A3)$v

+U1T<-t(svd(A3)$u)

+d<-svd(A3)$d

+sigma1<-matrix(c(1/d[1],0,0,0),ncol=2)

+A3inv<-2*(V1%*%sigma1%*%U1T)

+print("The Pseduo inverse of the given matrix")

+print(A3inv)
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