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Vector Spaces of Linearizations for Matrix Polynomials
TLDR
We show how to simply construct two vector spaces of pencils that generalize the companion forms of $P$, and prove that almost all of these pencils are linearizations for $P$. Expand
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Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
TLDR
In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored. Expand
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Symmetric Linearizations for Matrix Polynomials
TLDR
A standard way of treating the polynomial eigenvalue problem $P(\lambda)x = 0$ is to convert it into an equivalent matrix pencil—a process known as linearization. Expand
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Jordan structures of alternating matrix polynomials
Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. WeExpand
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Structured Factorizations in Scalar Product Spaces
TLDR
We study the structure in eigenvalues, eigenvectors, and singular values that persists across a wide range of scalar products of a scalar product when the product is factored. Expand
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Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem
  • N. Mackey
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1 April 1995
TLDR
A quaternion-Jacobi method in which the "weight" of four elements (in a $2 \times 2$ block) is transferred all at once onto the diagonal of a $4\times 4$ symmetric matrix. Expand
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Smith Forms of Palindromic Matrix Polynomials
Many applications give rise to matrix polynomials whose coefficients have a kind of reversal symmetry, a structure we call palindromic. Several properties of scalar palindromic polynomials areExpand
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On the Determinant of Symplectic Matrices
A collection of new and old proofs showing that the determinant of any symplectic matrix is +1 is presented. Structured factorizations of symplectic matrices play a key role in several arguments. AExpand
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Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
TLDR
A new family of coupled iterations for the matrix square root is derived. Expand
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G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces
We characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group Image and vectorsExpand
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