• Publications
• Influence
Vector Spaces of Linearizations for Matrix Polynomials
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 December 2006
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
• 293
• 37
• PDF
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 December 2006
In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored. Expand
• 249
• 19
• PDF
Symmetric Linearizations for Matrix Polynomials
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 December 2006
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
• 125
• 9
• PDF
Jordan structures of alternating matrix polynomials
• Mathematics
• 1 February 2010
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
• 43
• 5
• PDF
Structured Factorizations in Scalar Product Spaces
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 July 2005
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
• 67
• 4
• PDF
Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem
• N. Mackey
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 April 1995
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
• 37
• 4
Smith Forms of Palindromic Matrix Polynomials
• Mathematics
• 2011
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
• 48
• 4
• PDF
On the Determinant of Symplectic Matrices
• Mathematics
• 2003
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
• 27
• 4
• PDF
Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 1 March 2005
A new family of coupled iterations for the matrix square root is derived. Expand
• 56
• 3
• PDF
G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces
• Mathematics
• 1 July 2004
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
• 26
• 3
• PDF