# Engineering Analysis/Spectral Decomposition

If λ* _{i}* are the

*n*distinct eigenvalues of matrix

*A*, and

*v*are the corresponding n distinct eigenvectors, and if

_{i}*w*are the

_{i}*n*distinct left-eigenvectors, then the matrix

*A*can be represented as a sum:

this is known as the **spectral decomposition** of *A*.