In linear algebra the term "linear operator" most commonly refers to linear maps (i.e., functions preserving vector addition and scalar multiplication) that have the added peculiarity of mapping a vector space into itself (i.e., ). The term may be used with a different meaning in other ...
Linear Algebra & Its ApplicationsE. A. Carlen, R. L. Frank, and E. H. Lieb, Some operator and trace function convexity theorems, Linear Algebra ... Frank,Rupert,L.,... - 《Linear Algebra & Its Applications》 被引量: 9发表: 2016年 State-space realization of nonlinear input-output equ...
Hence, we can make definitions for continuous operators similar to their counterparts in linear algebra, including the following key classes of bilinear operators: • Self-adjoint: We call a bilinear form self-adjoint if ∀u, v : a(u, v) = a(v, u). This generalizes the definition ...
Krivulin N. K., and Romanovskii I.V.: On the convergence of matrix powers of a generalized linear operator in idempotent algebra. Journal of Mathematical Sciences, 142 (2007), 1 1806-1816.Romanovskii I.V.: On the convergence of matrix powers of a generalized linear operator in idempotent...
Let A be a partially ordered linear algebra, that is, it is a real linear algebra which has a directed partial ordering that is compatible with the algebraic structure. In this paper, the equation yx-xy=1 (x,y∈A) is studied. In particular, the following statements hold: (1) If xy-...
≠ L̂2L̂1The algebra of operators differs in this regard from the ordinary algebra of numbers. The possibility of changing the order of the factors in the product of two operators is closely connected with the possibility of the simultaneous measurement of the physical quantities to which ...
Stable controller design for the T-S fuzzy model of a flexible-joint robot arm based on Lie algebra In this paper, we develop a novel approach for the stability of T-S fuzzy systems using the Lie algebra generated by the linear subsystems used in the T-S ... E Gurkan,SP Banks,I ...
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but ...
This implies \sigma(b-a)\in \mathbb R^+ .Let H be a vector space. \sigma:H^2\to \mathbb C is called sesquilinear form if \sigma(\lambda x+y,z)=\lambda \sigma(x,z)+\sigma(y,z) and \sigma( x,\lambda y+z)=\bar{\lambda} \sigma(x,y)+\sigma(x,z) ....
Let T be a bounded linear operator on a Hilbert space H such that α[T∗,T]:=∑n=0∞αnT∗nTn≥0, where α(t)=∑n=0∞αntn is a suitable analytic function in the unit disc D with real coefficients. We prove that if α(t)=(1−t)α~(t), where α~ has no zeros ...