Answers to assignment 5

symmetric S[4,4]
            c1          c2          c3          c4
c1   18.833333
c2  -.33333333   11.333333
c3  -43.333333  -.66666667   157.33333
c4  -14.833333  -18.666667   43.333333   62.833333

symmetric C[4,4]
            c1          c2          c3          c4
c1   3.7666667
c2  -.06666667   2.2666667
c3  -8.6666667  -.13333333   31.466667
c4  -2.9666667  -3.7333333   8.6666667   12.566667

symmetric R[4,4]
            c1          c2          c3          c4
c1           1
c2  -.02281583           1
c3  -.79606427  -.01578772           1
c4  -.43120135  -.69950833   .43582955           1

determinants

determinant of S = 229312

determinant of C = 366.8992

determinant of R = .10867536


eigenvalues and eigenvectors


val1[1,4]:  eigenvalues S
           e1         e2         e3         e4
r1  186.95557  53.130987  6.9020295  3.3447502


vec1[4,4]:  eigenvectors S
            e1          e2          e3          e4
c1  -.26234205    .0568214   .86977755    .4140471
c2  -.04020873  -.37920143  -.38700488   .83953366
c3   .89801005  -.33647342   .28268041   .02133964
c4   .35091005   .86009491  -.11749905   .35113084


val2[1,4]:  eigenvalues C
           e1         e2         e3         e4
r1  37.391113  10.626197  1.3804059  .66895004


vec2[4,4]:  eigenvectors C
            e1          e2          e3          e4
c1  -.26234205    .0568214   .86977755    .4140471
c2  -.04020873  -.37920143  -.38700488   .83953366
c3   .89801005  -.33647342   .28268041   .02133964
c4   .35091005   .86009491  -.11749905   .35113084


val3[1,4]:  eigenvalues R
           e1         e2         e3         e4
r1  2.2380588  1.3851292  .20938862  .16742343


vec3[4,4]:  eigenvectors R
            e1          e2          e3          e4
c1  -.54052373  -.41881961    .5777944   .44562076
c2  -.31189314   .71878789  -.21916178   .58140756
c3   .54771082   .39379639   .73346656   .08345094
c4   .55728774  -.39097123  -.28310517    .6755911