Niloufer Mackey

Vector Spaces of Linearizations for Matrix Polynomials

The classical approach to investigating polynomial eigenvalue problems is linearization, where the polynomial is converted into a larger matrix pencil with the same eigenvalues. For any polynomial there are infinitely many linearizations with widely varying properties, but in practice the companion forms are typically used. However, these companion forms are not always entirely satisfactory, and linearizations with special properties may sometimes be required. Given a matrix polynomial

Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

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Symmetric Linearizations for Matrix Polynomials

, we develop a systematic approach to generating large classes of linearizations for

Structured Factorizations in Scalar Product Spaces

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STRUCTURED TOOLS FOR STRUCTURED MATRICES

. We show how to simply construct two vector spaces of pencils that generalize the companion forms of

Numerical methods for palindromic eigenvalue problems: Computing the anti‐triangular Schur form

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Smith forms of palindromic matrix polynomials

, and prove that almost all of these pencils are linearizations for

Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems☆

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HAMILTONIAN SQUARE ROOTS OF SKEW-HAMILTONIAN MATRICES

. Eigenvectors of these pencils are shown to be closely related to those of

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups

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