negative zero as eigenvalue
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Suma
el 10 de Abr. de 2014
Comentada: Suma
el 12 de Abr. de 2014
Hello,
Why do I get negative zero as eigenvalue?
ans =
0.2615 0.1950 - 0.3938i
0.1950 + 0.3938i 0.7384
>> eig(ans)
ans =
-0.0000
1.0000
thanks
2 comentarios
abhijit kulkarni
el 10 de Abr. de 2014
I think that negative zero implies that it is not treated as positive integer.
Refer: The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered as a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞; division is only undefined for ±0/±0 and ±∞/±∞.
Negatively signed zero echoes the mathematical analysis concept of approaching 0 from below as a one-sided limit, which may be denoted by x → 0−, x → 0−, or x → ↑0. The notation "−0" may be used informally to denote a small negative number that has been rounded to zero. The concept of negative zero also has some theoretical applications in statistical mechanics and other disciplines.
It is claimed that the inclusion of signed zero in IEEE 754 makes it much easier to achieve numerical accuracy in some critical problems,[1]
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Mischa Kim
el 10 de Abr. de 2014
Suma, it's not really zero. Set the display format to long fixed decimal:
format long
[v, d] = eig(a)
v =
0.381333979059441 - 0.770099081813373i 0.226935196532721 - 0.458292719972234i
-0.511401799571426 + 0.000000000000000i 0.859341724458383 + 0.000000000000000i
d =
-0.000011841043894 0
0 0.999911841043894
5 comentarios
Mischa Kim
el 10 de Abr. de 2014
i is the imaginary unit. Since the matrix is complex you can expect the eigenvectors to be complex as well.
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