Eigendecomposition of a Matrix
Learn about eigendecomposition using R, Rcpp, Armadillo, and Eigen.
Eigendecomposition, also called spectral decomposition, is the factorization of a matrix into a canonical form, where the matrix is represented in terms of its eigenvalues and eigenvectors.
- The matrix is a square matrix where the column is the eigenvector of .
- The matrix is the diagonal matrix where the diagonal elements are the corresponding eigenvalues .
Only diagonalizable matrices can be factorized in this way.
A (nonzero) vector of dimension n is an eigenvector of a square matrix if it satisfies the linear equation:
- The value is a scalar, termed the eigenvalue corresponding to the eigenvector .
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