Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices

Figure 4

Trajectories of 𝜙(𝑡)=−𝑥(𝑡)^𝑇(𝐴−𝐴^𝑇)²𝑥(𝑡)/4𝑥(𝑡)^𝑇𝑥(𝑡) and 𝜓(𝑡)=𝑥(𝑡)^𝑇(𝐴+𝐴^𝑇)𝑥(𝑡)/2𝑥(𝑡)^𝑇𝑥(𝑡) based on (10) with initial 𝑥(0) as (55), which should converge to |𝑏₃| and 𝑎₃, respectively.