Reduction of a Square Matrix to Triangular Form

1980 ◽  
Vol 64 (430) ◽  
pp. 266
Author(s):  
F. Gerrish
2019 ◽  
Vol 2 (1) ◽  
pp. 43-52
Author(s):  
Alireza Alikhani ◽  
Safa Dehghan M ◽  
Iman Shafieenejad

In this study, satellite formation flying guidance in the presence of under actuation using inter-vehicle Coulomb force is investigated. The Coulomb forces are used to stabilize the formation flying mission. For this purpose, the charge of satellites is determined to create appropriate attraction and repulsion and also, to maintain the distance between satellites. Static Coulomb formation of satellites equations including three satellites in triangular form was developed. Furthermore, the charge value of the Coulomb propulsion system required for such formation was obtained. Considering Under actuation of one of the formation satellites, the fault-tolerance approach is proposed for achieving mission goals. Following this approach, in the first step fault-tolerant guidance law is designed. Accordingly, the obtained results show stationary formation. In the next step, tomaintain the formation shape and dimension, a fault-tolerant control law is designed.


Laser Physics ◽  
2019 ◽  
Vol 29 (2) ◽  
pp. 025203 ◽  
Author(s):  
Xinwei Zha ◽  
Irfan Ahmed ◽  
Da Zhang ◽  
Wen Feng ◽  
Yanpeng Zhang

2021 ◽  
Vol 9 (1) ◽  
pp. 257-274
Author(s):  
Louis Deaett ◽  
Colin Garnett

Abstract Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A. A longstanding open question concerns the smallest possible number of nonzero entries in an n × n spectrally arbitrary pattern. The Generalized 2n Conjecture states that, for a pattern that meets an appropriate irreducibility condition, this number is 2n. An example of Shitov shows that this irreducibility is essential; following his technique, we construct a smaller such example. We then develop an appropriate algebraic condition and apply it computationally to show that, for n ≤ 7, the conjecture does hold for ℝ, and that there are essentially only two possible counterexamples over ℂ. Examining these two patterns, we highlight the problem of determining whether or not either is in fact spectrally arbitrary over ℂ. A general method for making this determination for a pattern remains a major goal; we introduce an algebraic tool that may be helpful.


1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.


2000 ◽  
Vol 45 (8) ◽  
pp. 1563-1569 ◽  
Author(s):  
Wei Xing ◽  
Qingling Zhang ◽  
Qiyi Wang
Keyword(s):  

The spectrum of the flame of carbon monoxide burning in air and in oxygen at reduced pressure has been photographed on plates of high contrast which display the band spectrum clearly above the continuous background. Greater detail has been obtained than has been recorded previously and new measurements are given. The structure of the spectrum has been studied systematically. It is shown that the bands occur in pairs with a separation of about 60 cm. -1 , this separation being due probably to the rotational structure. Various wave-number differences are found to occur frequently, and many of the strong bands are arranged in arrays using intervals of 565 and 2065 cm. -1 . The possible origin of the spectrum is discussed. The choice of emitter is limited to a polyatomic oxide of carbon, of which carbon dioxide is the most likely. The spectrum of the suboxide C 3 O 2 shows some resemblance to the flame bands, but this molecule is improbable as the emitter on other grounds. A peroxide C0 3 is also a possibility, but no evidence for the presence of this has been obtained from experiments on the slow combustion of carbon monoxide. Carbon dioxide in gaseous or liquid form is transparent through the visible and quartz ultra-violet, and the flame bands are not obtained from CO 2 in discharge tubes. Comparison with the Schumann-Runge bands of oxygen shows that it is possible that the flame bands may form part of the absorption band system of CO 2 which is known to exist below 1700 A if there is a big change in shape or size of the molecule in the two electronic states. The electronic energy levels of CO 2 are discussed. Since normal CO 2 is not built up from normal CO and oxygen, an electronic rearrangement of the CO 2 must occur after the combustion process. Mulliken has suggested that the molecule in the first excited electronic state, corresponding to absorption below 1700 A, may have a triangular form. The frequencies obtained from the flame bands are compared with the infra-red frequencies of CO 2 . The 565 interval may be identified with the transverse vibration v 2 , indicating that the excited electronic state is probably triangular in shape. The 2065 interval cannot, however, be identified with the asymmetric vibration v 3 with any certainty. If the excited electronic state of CO 2 is triangular, then molecules formed during the combustion by transitions from this level to the ground state may be “vibrationally activated”. This is probably the reason for many of the peculiarities of the combustion of carbon monoxide.


1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.


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