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