Special linear Lie algebraIn mathematics, the special linear Lie algebra of order n (denoted or ) is the Lie algebra of matrices with trace zero and with the Lie bracket . This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra is central to the study of special relativity, general relativity and supersymmetry: its fundamental representation is the so-called spinor representation, while its adjoint representation generates the Lorentz group SO(3,1) of special relativity.
SignalIn signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.
Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
Digital signal processorA digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio signal processing, telecommunications, , radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products. The goal of a DSP is usually to measure, filter or compress continuous real-world analog signals.
OriginalismIn the context of United States law, originalism is a theory of constitutional interpretation that asserts that all statements in the Constitution must be interpreted based on the original understanding. This concept views the Constitution as stable from the time of enactment and that the meaning of its contents can be changed only by the steps set out in Article Five. This notion stands in contrast to the concept of the Living Constitution, which asserts that the Constitution should be interpreted based on the context of current times, even if such interpretation is different from the original interpretations of the document.
Postgraduate educationPostgraduate education, graduate education, or grad school, refers to academic or professional degrees, certificates, diplomas, or other qualifications usually pursued by post-secondary students who have earned an undergraduate (bachelor's) degree. The organization and structure of postgraduate education varies in different countries, as well as in different institutions within countries.
BookA book is a medium for recording information in the form of writing or s, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. It can also be a handwritten or printed work of fiction or nonfiction, usually on sheets of paper fastened or bound together within covers. The technical term for this physical arrangement is codex (plural, codices). In the history of hand-held physical supports for extended written compositions or records, the codex replaces its predecessor, the scroll.
Spectral density estimationIn statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.
OriginalityOriginality is the aspect of created or invented works that distinguish them from reproductions, clones, forgeries, or substantially derivative works. The modern idea of originality is according to some scholars tied to Romanticism, by a notion that is often called romantic originality. The validity of "originality" as an operational concept has been questioned. For example, there is no clear boundary between "derivative" and "inspired by" or "in the tradition of." The concept of originality is both culturally and historically contingent.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Graduate diplomaA graduate diploma (GradD, GDip, GrDip, GradDip) is generally a qualification taken after completion of a first degree, although the level of study varies in different countries from being at the same level as the final year of a bachelor's degree to being at a level between a master's degree and a doctorate. In some countries the graduate diploma and postgraduate diploma are synonymous, while in others (particularly where the graduate diploma is at undergraduate degree level) the postgraduate diploma is a higher qualification.
Key events of the 20th centuryThe 20th century changed the world in unprecedented ways. The World Wars sparked tension between countries and led to the creation of atomic bombs, the Cold War led to the Space Race and the creation of space-based rockets, and the World Wide Web was created. These advancements have played a significant role in citizens' lives and shaped the 21st century into what it is today. From 1914 to 1918, the First World War, and its aftermath, caused major changes in the power balance of the world, destroying or transforming some of the most powerful empires.
