Solution of Linear Dynamical Systems
If the initial vector is aligned with a right eigenvector of the matrix, the dynamics are simple
where is the corresponding eigenvalue; the solution of this equation is
as may be confirmed by substitution.
If is diagonalizable, then any vector in an -dimensional space can be represented by a linear combination of the right and left eigenvectors (denoted ) of the matrix .
Therefore, the general solution for is a linear combination of the individual solutions for the right eigenvectors
Similar considerations apply to the discrete mappings.
Read more about this topic: Linear Dynamical System
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