08c848a3-cec3-417f-83cd-3bd077598685 26 6 6 decimal

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Function for calculating the coefficients of the characteristic polynomial, eigenvalues and eigenvectors

Adapted from: "Introduction to the use of SMath Studio" G. Urroz, May 2010

A eig n A rows : p n 1 matrix : I n identity : p n 1 + 1 el 1.0 - : B A : p n 1 el B tr : j n 1 - 1 n 2 - range B A B p j 1 + 1 el I * - (* : p j 1 el B tr n j - 1 + / : 21 line for p 1 - (n^p * : λ p polyroots : V n 1 - 1 matrix : j 1 n range A.L A λ j el I * - : A.Lm A.L 1 n 1 - 1 n 1 - submatrix : b.L A.L 1 n 1 - n n submatrix : x.L A.Lm 1 -^b.L * : V x.L V augment : 51 line for V V 1 n 1 - 1 n submatrix : V.b 1 n matrix : j 1 n range V.b 1 j el 1 : for V V V.b stack : j 1 n range x.L V j col : x.L x.L x.L norme / : V V x.L augment : 31 line for V V 1 n n 1 + 2 n * submatrix : p λ V 31 sys 181 line :

12 - 422 - 22 - 642 - 38268444 mat eig 1300 - 530 - 93101 - 51 mat 1.95 - 6.33 7.83 - 13.45 41 mat 0.35 - 0.1 0.79 0.7 - 0.21 - 0.51 0.52 - 0.46 0.59 - 0.57 0.26 0.54 - 0.69 0.64 0.18 0.11 44 mat 31 sys

2 - i + 0002 - i - 0001 - 33 mat eig 595141 mat 1 - 2 - i + 2 - i - 31 mat 00000011133 mat 31 sys

EIGENVECTORS CALCULATION FAILS FOR 2x2 MATRICES:

1 - 004 - 22 mat eig 1 el 4 - 5 - 1 - 31 mat

1 - 004 - 22 mat eig 2 el 1 - 4 - 21 mat

1 - i - 001 - i + 22 mat eig 1 el 2 - 2 - 1 - 31 mat

1 - i - 001 - i + 22 mat eig 2 el 1 - i + 1 - i - 21 mat

1 - 004 - 22 mat eig 3 el #

1 - i - 001 - i + 22 mat eig 3 el #