#EIGENVECTORS AND EIGENVALUES:

#MAKING MATRIX M:
M=matrix(c(5,-2,-3,2),nrow=2,ncol=2,byrow=T)
M

#COMPUTING EIGENVALUES AND EIGENVECTORS OF MATRIX M:
E=eigen(M)
E



#SHOWING EIGENVECTORS:
#FUNCTION make.grid() FINDS POINTS ON A GRID:
make.grid <- function(Xsize,Ysize){

ii=0
jj=0
X=numeric(0)
Y=numeric(0)

for(i in 1:Xsize) {
for(j in 1:Ysize) {
ii=ii+1
X[ii]=i
if(j==Ysize) j=0
jj=jj+1
Y[jj] = j
}
}

X
Y

M=cbind(X-mean(X),Y-mean(Y))
return(M)
}
1
X=make.grid(10,10)
M=matrix(c(1.0,0.3,0.3,1),nrow=2,ncol=2,byrow=T)1
E=eigen(M)

#LINEAR TRANSFORMATION:

Z=M%*%t(X)
Z=t(Z)

#PLOT TRANSFORMATION VECTORS:
plot(Z,type='n',xlab='X',ylab='Y')
arrows(X[,1],X[,2],Z[,1],Z[,2],col='purple',lwd=1,code=2,length=0.05)
arrows(0,0,8*E$vectors[,1],8*E$vectors[,2],col='red',code=2,length=0.05)