An eigendecomposition $A = P D P^{-1}$, with $D$ diagonal

Example · Undergraduate

Definition: eigendecomposition

Terms

Term	This example	Why
singular value decomposition	✗	An eigendecomposition $A = P D P^{-1}$ is not a singular value decomposition, because the columns of $P$ need not be orthonormal, and the eigenvalues in $D$ can be negative or complex. For a symmetric positive semidefinite matrix, the two decompositions coincide.

Distinctions using this example

• Types of matrix decompositions

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