References
149
x 2,2 + 3 x 2,3 = x 2,2
2 x 2,3 = x 2,3
for the components {x i,k } of x i since x 1,1 = 1 and x 1,2 = x 1,3 = 0. The last
equation implies x 2,3 = 0, a result that is consistent with the second equation. The
first equation with x 2,3 = 0 gives x 2,2 = 1 so that the components of x 2 are (0, 1, 0).
The vectors
x 1 , x 2 , x 3
span R 3 . The eigenvectors x 1 and x 2 are aligned with the
first coordinates of R 3 , while x 3 has non-zero projections on coordinates of this
space.
References
1. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers
(McGraw-Hill, New York, 1978)
2. R.L. Brabenec, Introduction to Real Analysis (PWS-KENT Publishing Company, Boston, 1990)
3. D.E. Goldberg, The Design of Innovation: Lessons from and for Competent Algorithms (Kluwer
Academic Publishers, Norwell, 2002)
4. D.A. Sánchez, Ordinary Differential Equations and Stability Theory: An Introduction (Dover
Publications Inc., Mineola, 1968)
5. G.P. Tolstov, Fourier Series (Dover Publications Inc., New York, 1962)