In the eigenvalue problem formulated in equation (2), q is an n x 1 unknown vector known as the eigenvector, or characteristic vector, or latent vector; [lambda] is an unknown scalar known as the eigenvalue, or

characteristic root, or latent root (Hoy, Livernois, McKenna, Rees, and Stengos, 1996).

The proportion of variation attributed to a particular principal component is obtained by dividing the associated

characteristic root by the sum of all the

characteristic roots.

Heck, Charts of Some Upper Percentage Points of the Distribution of the Largest

Characteristic Root, Ann.

When the

characteristic root for a regime is zero, there is an immediate jump to the attractor for that regime.

Letting [Lambda]be the

characteristic root of the dynamic system and linearing the system around the stationary equilibrium, we then have the following characteristic equation:

It is easy to verify from the entries in Table II that only one

characteristic root, derived from the correlation matrix of the five diffusion indexes, is greater than 0.

A permanent increase in productivity level ([Tau]) and a drop in interest rates (r) increase the new steady state value of capital and change the value of the

characteristic root, which, when the changes occur, lead to the upward jumps in the shadow price of capital (q), investment (i), output (f(k)), and consumption (c) instantaneously (and permanently).

This procedure relies on relationships between the rank of a matrix and its

characteristic roots (or eigenvalues).

So now the

characteristic roots are given by the following two equations

The Johansen 1988 method relies on the relationship between the rank of a matrix and its

characteristic roots (or eigenvalues).

2] are constants, which we call the

characteristic roots of (1.

and a is the minimum among the real parts of

characteristic roots to the right of -1.