A = PDP⁻¹
A = Original Matrix
P = Eigenvectors
D = Eigenvalues (Diagonal)
P⁻¹ = Inverse
Current Stage

Move the slider to see each step of A = PDP⁻¹ decomposition.

Why Diagonalization?

Diagonal matrices are computationally efficient - just multiply the diagonal elements. This decouples correlations and speeds up matrix powers: An = PDnP⁻¹

I P⁻¹ P⁻¹D PDP⁻¹
Eigenvector 1
Eigenvector 2
Basis î
Basis ĵ