Eigen Decomposition reveals the most important vector in the dataset, the Principal Component (also part of PCA).
Eigen Decomposition can be performed only on square matrices.
It extracts two features: Eigen Value (a lambda(scaler) that pre multiplies the Eigen Vector) and by reverse the Eigen Vector (a vector which post multiplies a matrix).
The EigenVector is in the null space of the pre multiplying matrix shifted on the identity matrix by the eigenvalue(s)(scalers). This shifted matrix must be a singular matrix to possess an(y) eigenvalue(s).
Formula:
(1:)Shift the matrix by lambda (by the identity matrix). (2:) Calculate the determinant. The result for lambda is the eigenvalue.
1: (A-λ)=0 —–> 2: |A-λI| = 0
The number of rows/cols in the squared matrix determines the number of eigenvalues.
