Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
TransposeIn linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. In the case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT.
Electronic toll collectionElectronic toll collection (ETC) is a wireless system to automatically collect the usage fee or toll charged to vehicles using toll roads, HOV lanes, toll bridges, and toll tunnels. It is a faster alternative which is replacing toll booths, where vehicles must stop and the driver manually pays the toll with cash or a card. In most systems, vehicles using the system are equipped with an automated radio transponder device.
Time travelTime travel is the hypothetical activity of traveling into the past or future. Time travel is a widely recognized concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a hypothetical device known as a time machine. The idea of a time machine was popularized by H. G. Wells' 1895 novel The Time Machine. It is uncertain if time travel to the past is physically possible, and such travel, if at all feasible, may give rise to questions of causality.
Time travel in fictionTime travel is a common theme in fiction, mainly since the late 19th century, and has been depicted in a variety of media, such as literature, television, film, and advertisements. The concept of time travel by mechanical means was popularized in H. G. Wells' 1895 story, The Time Machine. In general, time travel stories focus on the consequences of traveling into the past or the future.
Toll roadA toll road, also known as a turnpike or tollway, is a public or private road (almost always a controlled-access highway in the present day) for which a fee (or toll) is assessed for passage. It is a form of road pricing typically implemented to help recoup the costs of road construction and maintenance. Toll roads have existed in some form since antiquity, with tolls levied on passing travelers on foot, wagon, or horseback; a practice that continued with the automobile, and many modern tollways charge fees for motor vehicles exclusively.
Symplectic matrixIn mathematics, a symplectic matrix is a matrix with real entries that satisfies the condition where denotes the transpose of and is a fixed nonsingular, skew-symmetric matrix. This definition can be extended to matrices with entries in other fields, such as the complex numbers, finite fields, p-adic numbers, and function fields. Typically is chosen to be the block matrix where is the identity matrix. The matrix has determinant and its inverse is .
Temporal paradoxA temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility.
Probability mass functionIn probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
Probabilistic logicProbabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as in case of belief fusion in Dempster–Shafer theory.
