If the matrix A is symmetric, then A = V * D * V^T where the eigenvalue matrix D is a diagonal matrix and the eigenvector matrix V is orthogonal.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1 x 1 blocks and any complex eigenvalues (λ + i*μ) in 2 x 2 blocks ((λ, μ),(-μ, λ)). The columns of V represent the eigenvectors in the sense that A * V = V * D. The matrix V may be badly conditioned or even singular; so if the inverse of V can be computed depends on the condition number of V. (The condition number can be checked with SingularValueDecompositionD.)

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