Eigenvalue decomposition is a method of decomposing a square matrix into its eigenvectors and eigenvalues. Cholesky decomposition, on the other hand, is a method of decomposing a symmetric positive definite matrix into a lower triangular matrix and its transpose.
The choice between eigenvalue and Cholesky decomposition depends on the properties of your data. If your data is symmetric and positive definite, Cholesky decomposition is the better choice. However, if your data is not symmetric, eigenvalue decomposition is the only option.
No, Cholesky decomposition can only be used for symmetric positive definite matrices. Non-square matrices do not meet this requirement.
The eigenvalues and eigenvectors obtained from eigenvalue decomposition can be used to understand the linear transformation of the data. Cholesky decomposition results in a lower triangular matrix, which can be used to solve systems of linear equations.
Eigenvalue decomposition is more computationally intensive, but it provides a complete set of eigenvectors and eigenvalues. Cholesky decomposition is less computationally intensive and only requires the calculation of the lower triangular matrix. However, it is limited to symmetric positive definite matrices.