### Eigenvalue decomposition

An **eigenvalue decomposition** of a square matrix $A$ is a factorization in the form where $\Lambda$ is a diagonal matrix whose entries are the eigenvalues of $A$. Such a decomposition exists if and only if the matrix $A$ is **nondefective**, or if it has a full basis of eigenvectors.

# linear-algebra

# matrices

# matrix-factorization

# eigenpairs

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