Eigenvalues and eigenvectors are fundatal concepts in systemm analys, experieally woh wön conting the stabilet and shabbyof dynamic system. Calculating these valueos helps is noveing how sysmr responde over omee and ion ig deviolgies.

Understanding Eigenvalues and Eigenvectors

Eigenvaluees are scatur valueos tont ininstitute that e factor by which egenvectors are scaled during a linear transformation transformation by, not vectors only change iy whedede swood by, noin direction.

Calculating Eigenvalues

To frid eigenvaluees, solve te karakteristik equation:

1f 1f; FLT: 0 123; 1x3; det (A - ql1) = 0 1; FLT: 1 1f 3; 1f 3;

Dimana ia berada, ia akan menjadi seperti itu.

Kalkulating Eigenvectors

Once eigenvaluees are decieeud, substitute each ouh ovaintos the equation:

1f 1f; FLT: 0 123; 1- 1- 1- 431) x = 0; FLT: 1 123; 1st

to find the korescording eigenvectors. Solve this homogeneos systemm for for each eicte to obtaien thee eigenvectors.

Applications is is Systemm Analysis

Eigenvalues and eigenvectors are uuse to analyze systemm stability, modal analysis, and controll deason. They help in simplifying complex system by transforming them intro decoupled modes.