Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Calculating Eigencomponents

This is non-trivial. We can see this by noting that the property MCj = A y-6, -can be rewritten as [Pg.20]

The matrix [M — Ajl] must be of reduced rank to give a zero result when it multiplies a non-zero vector, and it therefore has a zero determinant. [Pg.20]

Thus Xj is a root of the equation, polynomial in A, det(M — XI) = 0 and computing the eigenvalues is equivalent to finding the roots of that polynomial, which is called the characteristic polynomial. [Pg.20]

Galois proved that this is non-trivial. If the size of M is greater than 4x4, then there is no algebraic closed form, and if the size of M is greater than 2x2 there is no practical closed form. [Pg.20]

Any algorithm for computing eigenvalues must therefore be iterative. The iteration might be hidden inside a polynomial solver or explicit (as in the QR algorithm) but it will always be there, unless some other information about the matrix can be exploited. [Pg.20]


Why do all the arithmetic of calculating eigencomponents, when there is software available to do it for us ... [Pg.88]


See other pages where Calculating Eigencomponents is mentioned: [Pg.20]    [Pg.21]    [Pg.20]    [Pg.21]    [Pg.283]    [Pg.260]   


SEARCH



Eigencomponents

© 2024 chempedia.info