# qreig1.s                         J F Monahan, June 2001
 # eigenvalues and vectors for some matrices
 # first problem
 A <- c(1, 3, 4, 3, 2, 8, 4, 8, 3)
 A <- matrix(A,3,3)
 "first matrix"
 A
 eigen(A)
 # second problem
 A <- c(1, -3, -2, 1, -3, 10, -3, 6, -2, -3, 3, -2,
        1, 6, -2, 1)
 A <- matrix(A,4,4)
 "second matrix"
 A
 eigen(A)
 # third problem
 A <- c(15, -1, -5, -3, 4, -1, 12, 3, 2, 3,
        -5, 3, 7, -1, 2, -3, 2, -1, 9, 1, 
         4, 3, 2, 1, 10)
 A <- matrix(A,5,5)
 "third matrix"
 A
 eigen(A)
 # fourth problem
 A <- c(8, -3, -2, 0, 6, 5, -3, 6, 1, -6, 0, -2,
        -2, 1, 5, -5, 2, 0, 0, -6, -5, 8, -3, -2,
        6, 0, 2, -3, 6, 1, 5, -2, 0, -2, 1, 5)
 A <- matrix(A,6,6)
 "fourth matrix -- three pairs of equal eigenvalues"
 A
 eigen(A)
 rm(list=ls())