Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
CommunicationCommunication is usually defined as the transmission of information. The term can also refer to the message itself, or the field of inquiry studying these transmissions, also known as communication studies. The precise definition of communication is disputed. Controversial issues are whether unintentional or failed transmissions are included and whether communication does not just transmit meaning but also create it. Models of communication aim to provide a simplified overview of its main components and their interaction.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Algebra representationIn abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
Interpersonal communicationInterpersonal communication is an exchange of information between two or more people. It is also an area of research that seeks to understand how humans use verbal and nonverbal cues to accomplish a number of personal and relational goals. Interpersonal communication research addresses at least six categories of inquiry: 1) how humans adjust and adapt their verbal communication and nonverbal communication during face-to-face communication; 2) how messages are produced; 3) how uncertainty influences behavior and information-management strategies; 4) deceptive communication; 5) relational dialectics; and 6) social interactions that are mediated by technology.
Organizational communicationWithin the realm of communication studies, organizational communication is a field of study surrounding all areas of communication and information flow that contribute to the functioning of an organization . Organizational communication is constantly evolving and as a result, the scope of organizations included in this field of research have also shifted over time. Now both traditionally profitable companies, as well as NGO's and non-profit organizations, are points of interest for scholars focused on the field of organizational communication.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
Public participationPublic participation, also known as citizen participation or patient and public involvement, is the inclusion of the public in the activities of any organization or project. Public participation is similar to but more inclusive than stakeholder engagement. Generally public participation seeks and facilitates the involvement of those potentially affected by or interested in a decision. This can be in relation to individuals, governments, institutions, companies or any other entities that affect public interests.
Models of communicationModels of communication are simplified representations of the process of communication. Most models try to describe both verbal and non-verbal communication and often understand it as an exchange of messages. Their function is to give a compact overview of the complex process of communication. This helps researchers formulate hypotheses, apply communication-related concepts to real-world cases, and test predictions. Despite their usefulness, many models are criticized based on the claim that they are too simple because they leave out essential aspects.
GovernanceGovernance is the process of making and enforcing decisions within an organization or society. It is the process of interactions through the laws, social norms, power (social and political) or language as structured in communication of an organized society over a social system (family, social group, formal or informal organization, a territory under a jurisdiction or across territories). It is done by the government of a state, by a market, or by a network.
OrganizationAn organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from the Greek word organon, which means tool or instrument, musical instrument, and organ. There are a variety of legal types of organizations, including corporations, governments, non-governmental organizations, political organizations, international organizations, armed forces, charities, not-for-profit corporations, partnerships, cooperatives, and educational institutions, etc.
Communication studiesCommunication studies or communication science is an academic discipline that deals with processes of human communication and behavior, patterns of communication in interpersonal relationships, social interactions and communication in different cultures. Communication is commonly defined as giving, receiving or exchanging ideas, information, signals or messages through appropriate media, enabling individuals or groups to persuade, to seek information, to give information or to express emotions effectively.
Public participation (decision making)Citizen Participation or Public Participation in social science refers to different mechanisms for the public to express opinions—and ideally exert influence—regarding political, economic, management or other social decisions. Participatory decision-making can take place along any realm of human social activity, including economic (i.e. participatory economics), political (i.e. participatory democracy or parpolity), management (i.e. participatory management), cultural (i.e. polyculturalism) or familial (i.
EngagementAn engagement or betrothal is the period of time between the declaration of acceptance of a marriage proposal and the marriage itself (which is typically but not always commenced with a wedding). During this period, a couple is said to be fiancés (from the French), betrothed, intended, affianced, engaged to be married, or simply engaged. Future brides and grooms may be called fiancée (feminine) or fiancé (masculine), the betrothed, a wife-to-be or husband-to-be, respectively.
Engagement ringAn engagement ring, also known as a betrothal ring, is a ring indicating that the person wearing it is engaged to be married, especially in Western cultures. A ring is presented as an engagement gift by a partner to their prospective spouse when they propose marriage or directly after a marriage proposal is accepted. It represents a formal agreement to future marriage. In most Western countries, engagement rings are worn mostly by women, and rings can feature diamonds or other gemstones.
Organizational behaviorOrganizational behavior or organisational behaviour (see spelling differences) is the: "study of human behavior in organizational settings, the interface between human behavior and the organization, and the organization itself". Organizational behavioral research can be categorized in at least three ways: individuals in organizations (micro-level) work groups (meso-level) how organizations behave (macro-level) Chester Barnard recognized that individuals behave differently when acting in their organizational role than when acting separately from the organization.
Global governanceGlobal governance refers to institutions that coordinate the behavior of transnational actors, facilitate cooperation, resolve disputes, and alleviate collective action problems. Global governance broadly entails making, monitoring, and enforcing rules. Within global governance, a variety of types of actors – not just states – exercise power. Governance is thus broader than government. Global governance began in the mid-19th century. It became particularly prominent in the aftermath of World War I, and more so after the end of World War II.
Animal communicationAnimal communication is the transfer of information from one or a group of animals (sender or senders) to one or more other animals (receiver or receivers) that affects the current or future behavior of the receivers. Information may be sent intentionally, as in a courtship display, or unintentionally, as in the transfer of scent from predator to prey with kairomones. Information may be transferred to an "audience" of several receivers. Animal communication is a rapidly growing area of study in disciplines including animal behavior, sociology, neurology and animal cognition.
Organization developmentOrganization development (OD) is the study and implementation of practices, systems, and techniques that affect organizational change. The goal of which is to modify a group's/organization's performance and/or culture. The organizational changes are typically initiated by the group's stakeholders. OD emerged from human relations studies in the 1930s, during which psychologists realized that organizational structures and processes influence worker behavior and motivation.
