Chapter E - Eigenvalues

Problem C24

Using R

A = matrix(c(1,-1,1,-1,1,-1,1,-1,1), nrow=3, ncol=3, byrow = T)

A

##      [,1] [,2] [,3]
## [1,]    1   -1    1
## [2,]   -1    1   -1
## [3,]    1   -1    1

Av <- eigen(A)
Av

## eigen() decomposition
## $values
## [1] 3.000000e+00 8.881784e-16 0.000000e+00
## 
## $vectors
##            [,1]       [,2]      [,3]
## [1,]  0.5773503 -0.8164966 0.0000000
## [2,] -0.5773503 -0.4082483 0.7071068
## [3,]  0.5773503  0.4082483 0.7071068

The Eigen values are

3.000000e+00 8.881784e-16 0.000000e+00

Eigen vectors

$vectors [,1] [,2] [,3] [1,] 0.5773503 -0.8164966 0.0000000 [2,] -0.5773503 -0.4082483 0.7071068 [3,] 0.5773503 0.4082483 0.7071068