Hadamard variation formula

In matrix theory, the Hadamard variation formula is a set of differential equations for how the eigenvalues of a time-varying Hermitian matrix with distinct eigenvalues change with time.

Statement

Consider the space of $n\times n$ Hermitian matrices with all eigenvalues distinct.

Let $A=A(t)$ be a path in the space. Let $u_i,{\lambda }_i$ be its eigenpairs.

Template:Math proofTemplate:Hidden endHigher order generalizations appeared in Template:Harvard citation.

References

• Template:Cite journal
• Template:Cite book