in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

This paper studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary condition and a sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI ...

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of cohe...

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...

A = aerodynamic stiffness matrix C = speed of sound E = complex Fourier matrix f , F = physical and modal forces h = height of stream tube j = imaginary unit K, M = stiffness and mass matrices NB = number of blades P, Q = modal transformation matrices p = flow pressure Q = flow mass flux at the boundary q = generalized (modal) coordinate s = distance along the boundary T = period of flow unstea...

The infinite matrices in Witten’s vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s = 0 limit. We find that s = 1 eigenfunctions just acquire a p term, and x gets rep...

Gregory S. Chirikjian Johns Hopkins University 2.1 Rotations in Three Dimensions Rules for Composing Rotations • Euler Angles • The Matrix Exponential 2.2 Full Rigid-Body Motion Composition of Motions • Screw Motions 2.3 Homogeneous Transforms and the Denavit-Hartenberg Parameters Homogeneous Transformation Matrices • The Denavit-Hartenberg Parameters in Robotics 2.4 Infinitesimal Motions and A...

We introduce a simple uniform structure of elementary Φ-unitary matrices. Elementary Φ-unitary transformations are the extentions of Householder transformations in real and complex spaces with a definite or an indefinite inner product induced by a nonsingular signature matrix Φ. The extentions are found useful in the computations of complex matrices or special structured matrices. For two (comp...

It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree ...