Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Unified Modeling LanguageThe unified modeling language (UML) is a general-purpose visual modeling language that is intended to provide a standard way to visualize the design of a system. UML provides a standard notation for many types of diagrams which can be roughly divided into 3 main groups: behavior diagrams, interaction diagrams, and structure diagrams. The creation of UML was originally motivated by the desire to standardize the disparate notational systems and approaches to software design.
Kalman filterFor statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.
Discrete-time Fourier transformIn mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
Object-modeling languageAn object-modeling language is a standardized set of symbols used to model a software system using an object-oriented framework. The symbols can be either informal or formal ranging from predefined graphical templates to formal object models defined by grammars and specifications. A modeling language is usually associated with a methodology for object-oriented development. The modeling language defines the elements of the model. E.g., that a model has classes, methods, object properties, etc.
Systems modeling languageThe systems modeling language (SysML) is a general-purpose modeling language for systems engineering applications. It supports the specification, analysis, design, verification and validation of a broad range of systems and systems-of-systems. SysML was originally developed by an open source specification project, and includes an open source license for distribution and use. SysML is defined as an extension of a subset of the Unified Modeling Language (UML) using . The language's extensions were designed to support systems engineering activities.
General-purpose modelingGeneral-purpose modeling (GPM) is the systematic use of a general-purpose modeling language to represent the various facets of an object or a system. Examples of GPM languages are: The Unified Modeling Language (UML), an industry standard for modeling software-intensive systems EXPRESS, a data modeling language for product data, standardized as ISO 10303-11 IDEF, a group of languages from the 1970s that aimed to be neutral, generic and reusable Gellish, an industry standard natural language oriented modeling language for storage and exchange of data and knowledge, published in 2005 XML, a data modeling language now beginning to be used to model code (MetaL, Microsoft .
Attention (machine learning)Machine learning-based attention is a mechanism mimicking cognitive attention. It calculates "soft" weights for each word, more precisely for its embedding, in the context window. It can do it either in parallel (such as in transformers) or sequentially (such as recursive neural networks). "Soft" weights can change during each runtime, in contrast to "hard" weights, which are (pre-)trained and fine-tuned and remain frozen afterwards. Multiple attention heads are used in transformer-based large language models.
Domain-specific modelingDomain-specific modeling (DSM) is a software engineering methodology for designing and developing systems, such as computer software. It involves systematic use of a domain-specific language to represent the various facets of a system. Domain-specific modeling languages tend to support higher-level abstractions than general-purpose modeling languages, so they require less effort and fewer low-level details to specify a given system.
Algorithmic efficiencyIn computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. An algorithm must be analyzed to determine its resource usage, and the efficiency of an algorithm can be measured based on the usage of different resources. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process. For maximum efficiency it is desirable to minimize resource usage.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
