Linear time-invariant systemIn system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).
Del (command)In computing, del (or erase) is a command in command-line interpreters (shells) such as COMMAND.COM, cmd.exe, 4DOS, NDOS, 4OS2, 4NT and Windows PowerShell. It is used to delete one or more or from a . The command is available for various operating systems including DOS, Microware OS-9, IBM OS/2, Microsoft Windows and ReactOS. It is analogous to the Unix rm command and to the Stratus OpenVOS delete_file and delete_dircommands. DEC RT-11, OS/8, RSX-11, and OpenVMS also provide the delete command which can be contracted to del.
Trash (computing)In computing, the trash is a graphical user interface desktop metaphor for temporary storage for set aside by the user for deletion, but not yet permanently erased. The concept and name is part of Mac operating systems, a similar implementation is called the Recycle Bin in Microsoft Windows, and other operating systems use other names. In the , the trash can be viewed by the user as a special file directory, allowing the user to browse the files and retain those still wanted before deleting the others permanently (either one by one, or via an "empty trash" command).
Gaussian quadratureIn numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. (See numerical integration for more on quadrature rules.) An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the nodes x_i and weights w_i for i = 1, ..., n.
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.
Home directoryA home directory is a on a multi-user operating system containing for a given user of the system. The specifics of the home directory (such as its name and location) are defined by the operating system involved; for example, Linux / BSD () systems use /home/ or /usr/home/ and Windows systems between 2000 and Server 2003 keep home directories in a folder named Documents and Settings. A user's home directory is intended to contain that user's files; including text documents, music, pictures, videos, etc.
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.
Carl Friedrich GaussJohann Carl Friedrich Gauss (Gauß kaʁl ˈfʁiːdʁɪç ˈɡaʊs; Carolus Fridericus Gauss; 30 April 1777 23 February 1855) was a German mathematician, geodesist, and physicist who made significant contributions to many fields in mathematics and science. Gauss ranks among history's most influential mathematicians. Gauss was a child prodigy in mathematics, attended Collegium Carolinum, and, while studying at the University of Göttingen, made several important mathematical discoveries.
Chebyshev polynomialsThe Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as and . They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind are defined by Similarly, the Chebyshev polynomials of the second kind are defined by That these expressions define polynomials in may not be obvious at first sight, but follows by rewriting and using de Moivre's formula or by using the angle sum formulas for and repeatedly.
Toeplitz matrixIn linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix: Any matrix of the form is a Toeplitz matrix. If the element of is denoted then we have A Toeplitz matrix is not necessarily square. A matrix equation of the form is called a Toeplitz system if is a Toeplitz matrix. If is an Toeplitz matrix, then the system has at-most only unique values, rather than .
Nonlinear systemIn mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
