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.
Alfred and EmilyAlfred and Emily is a book by Doris Lessing in a new hybrid form. Part fiction, part notebook, part memoir, it was first published in 2008. The book is based on the lives of Lessing's parents. Part one is a novella, a fictional portrait of how her parents' lives might have been without the interruption of the First World War. Part two is a retelling of how her parents' lives really developed. The novella begins in England in 1902, when Alfred and Emily meet at a cricket match.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
Tom Friedman (artist)Tom Friedman (born 1965) is an American conceptual sculptor. He was born in St. Louis, Missouri and received a BFA in graphic illustration from Washington University in St. Louis (1988) and an MFA in sculpture from the University of Illinois at Chicago (1990.). As a conceptual artist he works in diverse media including sculpture, painting, drawing, video, and installation. For over twenty years, Friedman has been investigating the viewer/object relationship, and "the space in between.
Fritz the CatFritz the Cat is a comic strip created by Robert Crumb. Set in a "supercity" of anthropomorphic animals, it focused on Fritz, a tabby cat who frequently went on wild adventures that sometimes involved sexual escapades. Crumb began drawing the character in homemade comic books as a child. Fritz became one of his best-known characters, thanks largely to the motion picture adaptation by Ralph Bakshi.
Frank PiatekFrank Piatek (born 1944) is an American artist, known for abstract, illusionistic paintings of tubular forms and three-dimensional works exploring spirituality, cultural memory and the creative process. Piatek emerged in the mid-1960s, among a group of Chicago artists exploring various types of organic abstraction that shared qualities with the Chicago Imagists; his work, however relies more on suggestion than expressionistic representation.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
ObservabilityObservability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by the Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system.
Robert KlippelRobert Klippel AO (19 June 1920 19 June 2001) was an Australian constructivist sculptor and teacher. He is often described in contemporary art literature as Australia's greatest sculptor. Throughout his career he produced some 1,300 pieces of sculpture and approximately 5,000 drawings. Klippel was born in Potts Point, Sydney on 19 June 1920. At the age of six, he made his first model ship after being taken on a ferry ride on Sydney Harbour. Model making became a passion. He was educated at Sydney Grammar School.
Linear systemIn systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.
Control engineeringControl engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance.
Control systemA control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
System analysisSystem analysis in the field of electrical engineering characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio speakers; electrical engineers often use it because of its direct relevance to many areas of their discipline, most notably signal processing, communication systems and control systems. A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals.
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).
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Standard basisIn mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction.
Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
Transfer functionIn engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. They are widely used in electronic engineering tools like circuit simulators and control systems. In some simple cases, this function can be represented as two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve.
