Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

A fundamental bound for a Hadamard multiplier operator of Cauchy t ype implies a known bound on the inverse of the operator T : X ! AX ,XBas well as a general perturbation bound involving the unitary factor in the polar decomposition; the latter bound leads to a perturbation bound on the positive semideenite factor.

For any matrix automorphism group G associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of A ∈ G also lie in G; moreover, the polar factors of A lie in G if the matrix of the underlying form is unitary. Groups satisfying the latter condition include the complex orthogonal, real and complex symplectic, and ps...

Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU2. Numerous examples are given for d = 2, 3 and 4.

The problem of efficient soft-decision decoding of polar codes with ReedSolomon kernel is considered. A decomposition of the kernel based on the cyclotomic FFT algorithm is proposed, which enables one to implement near-optimal evaluation of log-likelihood ratios in the successive cancellation decoding algorithm.

We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [1–3] can be regarded as compact formulations by using the polar decomposition of the complex link fields. In particular, the gauge part of the supersymmetric lattice action is the standard Wilson action. This formulation facilitates the construction of gauge invariant operators.

For a given real invertible skew-symmetric matrix H, we characterize the real 2n×2n matrices X that allow an H-Hamiltonian polar decomposition of the type X = UA, where U is a real H-symplectic matrix (UTHU = H) and A is a real H-Hamiltonian matrix (HA = −ATH).

We present a decomposition theorem of the generic polar curves generalized curve foliation with only one separatrix and Hamiltonian foliations defined by approximate roots generatrix. This is generalization to Jacobians given García Barroso Gwoździewicz for plane branches.

Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field F22m seems to be a promising approach since Tu and Deng’s work. In this paper, we consider the same problem in a new way. Based on polar decomposition of the multiplicative group of F22m , we propose a new construction of Boolean functions with optimal algebrai...

-In this paper we use the parameteric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second direc...