Matrix calculusIn mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations.
Language processing in the brainIn psycholinguistics, language processing refers to the way humans use words to communicate ideas and feelings, and how such communications are processed and understood. Language processing is considered to be a uniquely human ability that is not produced with the same grammatical understanding or systematicity in even human's closest primate relatives. Throughout the 20th century the dominant model for language processing in the brain was the Geschwind-Lichteim-Wernicke model, which is based primarily on the analysis of brain-damaged patients.
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.
Output deviceAn output device is a piece of computer hardware that converts information into a human-perceptible form or, historically, into a physical machine-readable form for use with other non-computerized equipment. It can be text, graphics, tactile, audio, or video. Examples include monitors, printers, speakers, headphones, projectors, GPS devices, optical mark readers, and braille readers.
Digital signalA digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values. Simple digital signals represent information in discrete bands of analog levels. All levels within a band of values represent the same information state.
Linear subspaceIn mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. If V is a vector space over a field K and if W is a subset of V, then W is a linear subspace of V if under the operations of V, W is a vector space over K.
Design methodsDesign methods are procedures, techniques, aids, or tools for designing. They offer a number of different kinds of activities that a designer might use within an overall design process. Conventional procedures of design, such as drawing, can be regarded as design methods, but since the 1950s new procedures have been developed that are more usually grouped together under the name of "design methods". What design methods have in common is that they "are attempts to make public the hitherto private thinking of designers; to externalise the design process".
Speech repetitionSpeech repetition occurs when individuals speak the sounds that they have heard another person pronounce or say. In other words, it is the saying by one individual of the spoken vocalizations made by another individual. Speech repetition requires the person repeating the utterance to have the ability to map the sounds that they hear from the other person's oral pronunciation to similar places and manners of articulation in their own vocal tract.
Matrix mechanicsMatrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation.
Linear algebraic groupIn mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation where is the transpose of . Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(n,R).
Pauli matricesIn mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.
S-matrixIn physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states.
