Eigen Decomposition of a Matrix
- Eigen decomposition, also known as spectral decomposition, is a process of decomposing a matrix into its constituent eigenvectors and eigenvalues.
- In linear algebra, eigenvectors and eigenvalues are used to describe the behavior of a linear transformation on a vector space.
- Eigenvectors are the non-zero vectors that only change in magnitude when a linear transformation is applied to them, while eigenvalues are the scalars that represent the amount of scaling that occurs when the linear transformation is applied to the eigenvectors. The eigen decomposition of a matrix A is given by the equation: A = Q Λ Q^-1
where,
Q is a matrix whose columns are the eigenvectors of A
Λ is a diagonal matrix whose entries are the corresponding eigenvalues of A
Q^-1 is the inverse of Q