Workshop on Matrices and Operators July 13 , 2007 T 5 , Meng Wah Complex The University of Hong Kong
نویسندگان
چکیده
In this talk, we give a criterion for a companion matrix to be reducible and give a complete characterization of reducible companion matrices. We also consider properties of the numerical ranges of reducible companion matrices. To be more precise, if C is an n-by-n reducible companion matrix which is unitarily equivalent to the direct sum of A and B, we study properties of the numerical ranges of these direct summands A and B. We show that the boundary of such a numerical range is a differentiable algebraic curve. We also obtain a criterion for the equality W (C) = W (A).
منابع مشابه
Anxiety symptoms associated with problematic smartphone use severity: The mediation role of COVID-19 anxiety
Background: The Coronavirus Disease 2019 (COVID-19) pandemic is regarded as the biggest global health crisis in recent decades. The changes in major life domains due to infection control strategies resemble the functional impairment consequential to emotional distress and place many people at greater risk of psychiatric conditions. Meanwhile, the COVID-19 pandemic and associated social distanci...
متن کاملHealing of Complete Tear of the Anterior Talofibular Ligament and Early Ankle Stabilization after Autologous Platelet Rich Plasma: a Case Report and Literature Review
Lateral Ankle sprain (LAS) is a common sports injury associated with recurrent ankle sprain, chronic ankle instability(CAI) and post-traumatic ankle osteoarthritis (PTOA). Platelet Rich Plasma (PRP) has been increasingly used forherapeutic applications in sports-related injuries, and is thought to stimulate tissue healing. We reported a case ofLAS with complete tear of anterior talofibular liga...
متن کاملA Case Series of Life-Threatening MDMA Poisoning in An Electronic Dance Music Party in Hong Kong
Background: MDMA (3,4-methylenedioxymethamphetamine), which is also known as Ecstasy or Molly, is a commonly found abusive agent in Hong Kong. MDMA abuse is widely reported in electronic dance music (EDM) festivals all over the world. It brings about uncommon mortality and serious morbidity with recreational use, which are believed to be related to serotonin toxicity. Cyproheptadine has anti-hi...
متن کاملThe Contribution of Ageing to Hospitalisation Days in Hong Kong: A Decomposition Analysis
Background Ageing has become a serious challenge in Hong Kong and globally. It has serious implications for health expenditure, which accounts for nearly 20% of overall government expenditure. Here we assess the contribution of ageing and related factors to hospitalisation days in Hong Kong. We used hospital discharge data from all publicly funded hospitals in Hong Kong between 2001 and 2012. ...
متن کاملHeritage Conservationin Hong kong (Policy and Planning Context Review)
Since the enactment of the Antiquities and Monuments Ordinance in 1971 and the establishment of Antiquities and Monuments Office in 1976, the Hong Kong Government has set up several institutions with particular ordinances and schemes for Heritage Conservation. With the set-up of government initiatives, yet the protection of physical and cultural heritage is still limited due to the ambiguity of...
متن کامل