<content> Extracting individual eigen vectors </content>

f528a377-7764-4781-ab97-c90204da9dcd 46 Dr Chittaranjan Ghosh 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

A 0.115 8.5628 1018 -^* - 0.1636 2.7401 1017 -^* - 0.0545 8.5628 1018 -^* - 0.3434 3.2696 1017 -^* - 0.2181 9.7861 1018 -^* 0.1636 3.2696 1017 -^* - 0.5059 0 0.1636 2.7401 1017 -^* - 0.2181 0 0.6025 2.4219 1017 -^* 0.0545 9.7861 1018 -^* 0.1636 2.4219 1017 -^* 0.7641 55 mat :

To find eigenvalues and eigenvetors:

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 Aλ A λ j el I * - : Aλm Aλ 1 n 1 - 1 n 1 - submatrix : bλ Aλ 1 n 1 - n n submatrix - : xλ Aλm 1 -^bλ * : V xλ V augment : 51 line for V V 1 n 1 - 1 n submatrix : Vb 1 n matrix : j 1 n range Vb 1 j el 1 : for V V Vb stack : j 1 n range xλ V j col : xλ xλ xλ norme / : V V xλ augment : 31 line for V V 1 n n 1 + 2 n * submatrix : 171 line

p 0.0036 - 0.097 0.6934 - 1.9455 2.3309 - 161 mat

λ 0.0555 0.2193 0.4658 0.7266 0.8637 51 mat

Eigen value component

λ 1 el 0.0555

λ 4 el 0.7266

Coefficients

Eigen values

λ 2 el 0.2193

λ 5 el 0.8637

λ 3 el 0.4658

Eigen vectors

V 0.1661 0.245 0.301 - 0.1755 - 0.939 1.5765 1017 -^* 2.1376 106 -^* - 3.282 1018 -^* 0.0002 6.6988 1017 -^* - 0.4719 0.6879 0.8119 - 0.4148 - 0.3437 - 7.6018 1017 -^* 3.756 106 -^* - 1.5414 1016 -^* - 0.0001 - 7.3438 1017 -^* 0.8659 0.6832 0.5002 0.8928 0.0071 55 mat

<content> Extracting individual eigen vectors </content>

x1 V 1 col :

x2 V 2 col :

x3 V 3 col :

x4 V 4 col :

x1 0.1661 1.5765 1017 -^* 0.4719 7.6018 1017 -^* 0.8659 51 mat

x2 0.245 2.1376 106 -^* - 0.6879 3.756 106 -^* - 0.6832 51 mat

x3 0.301 - 3.282 1018 -^* 0.8119 - 1.5414 1016 -^* - 0.5002 51 mat

x4 0.1755 - 0.0002 0.4148 - 0.0001 - 0.8928 51 mat

x5 V 5 col :

x5 0.939 6.6988 1017 -^* - 0.3437 - 7.3438 1017 -^* 0.0071 51 mat

<content> To check orthogonality and orthonormality </content>

x1 transpose x2 * 0.9569 11 mat

x1 norme 1

x1 transpose x1 * 111 mat

x1 transpose x3 * 5.5472 1013 -^* 11 mat

x2 norme 1

x2 transpose x2 * 111 mat

x3 norme 1

x3 transpose x3 * 111 mat

x1 transpose x4 * 0.5482 11 mat

OR

x4 norme 1

x4 transpose x4 * 111 mat

x1 transpose x5 * 5.6831 1013 -^* 11 mat

x5 norme 1

x5 transpose x5 * 111 mat

x2 transpose x3 * 0.2905 - 11 mat