Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b, linear functions such as ↦ a 1 x 1 + … + a n x n, their representations in vector spaces and through matrices. Linear algebra is central to all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines and rotations. Functional analysis may be viewed as the application of linear algebra to spaces of functions. Linear algebra is used in most sciences and engineering areas, because it allows modeling many natural phenomena, efficiently computing with such models. For nonlinear systems, which cannot be modeled with linear algebra, linear algebra is used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point; the procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art.
Its use is illustrated with two to five equations. Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry and planes are represented by linear equations, computing their intersections amounts to solving systems of linear equations; the first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Gauss further described the method of elimination, listed as an advancement in geodesy. In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, Latin for womb. Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in ℂ have a difference w – z, the line segments w z ¯ and 0 ¯ are of the same length and direction.
The segments are equipollent. The four-dimensional system ℍ of quaternions was started in 1843; the term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q produces a segment equipollent to p q ¯. Other hypercomplex number systems used the idea of a linear space with a basis. Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group; the mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object, he realized the connection between matrices and determinants, wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants". Benjamin Peirce published his Linear Associative Algebra, his son Charles Sanders Peirce extended the work later; the telegraph required an explanatory system, the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression.
Linear algebra serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, much of the history of linear algebra is the history of Lorentz transformations; the first modern and more precise definition of a vector space was introduced by Peano in 1888. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra; the development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, linear algebra became an essential tool for modelling and simulations. See Determinant § History and Gaussian elimination § History; until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is preferred, since it is more synthetic, more general, conceptually simpler, although more abstract.
A vector space over a field F is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, elements of F are called scalars; the first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any s
Unión Deportiva Vall de Uxó is a football team based in La Vall d'Uixó, in Castellón province, autonomous community of Valencian Community, Spain. Founded in 1975, it plays in Regional Preferente – Group 1, its stadium is José Mangriñán. Unión Deportiva Vall de Uxó was founded in 1975. There was another club from La Vall d'Uixó, CD Piel, but only played in regional divisions. CD Piel was dissolved in 1975. 3 seasons in Segunda División B 16 seasons in Tercera División José Manuel Pesudo Official website Futbolme.com profile
Aristotle George "Harry" Agganis, nicknamed "The Golden Greek", was an American college football player and professional baseball player. After passing up a potential professional football career, he played in Major League Baseball as a first baseman from 1954 to 1955 for the Boston Red Sox. Born in Lynn, Massachusetts to Greek immigrants, Georgios Agganis and Georgia Papalimperis, Agganis first gained notice as a college football player at Boston University, becoming the first person in school history to be named All-American, he passed up a professional career with the Cleveland Browns in order to play his favorite sport, close to his hometown. Agganis was signed to a bonus baby contract, after one season playing minor league baseball, Agganis became the starter at first base for the Red Sox. In 1955, Agganis became gravely ill early in the season and was hospitalized for two weeks for pneumonia, he rejoined the Red Sox for a single week before being rehospitalized with a viral infection. After showing some signs of recovery, Agganis died of a pulmonary embolism on June 27.
Agganis' sudden death is considered one of the greatest tragedies to hit Boston's sporting community. Agganis' Greek immigrant family were from Longanikos, Greece, he was born in Massachusetts, to a large family which includes four brothers and two sisters. He was a star football and baseball player at Lynn Classical High School as well as a strong student, being named as "All-Scholastic" from the state of Massachusetts. Agganis enrolled at Boston University, where he became a starter at quarterback. After his sophomore season in 1949, when he set a school record by tossing fifteen touchdown passes, he entered the Marine Corps. Agganis played for baseball teams, he received a dependency discharge from the Marines to support his mother and returned to college to play in 1951-52. Around the same time, Agganis was participating in summer baseball leagues in Maine. Agganis became the school's first All-American in football and Boston coach Buff Donelli named Agganis the "greatest football player he coached".
He played basketball and baseball in the school. Agganis set another Boston University mark by passing for 1,402 yards for the season and won the Bulger Lowe Award as New England's outstanding football player. Coach Paul Brown of the Cleveland Browns thought he could be the successor to Otto Graham and drafted the college junior in the first round of the 1952 NFL Draft, offering him a bonus of $25,000. Boston Red Sox owner Tom Yawkey outbid Brown and signed Agganis to play Major League Baseball for the Red Sox as a first baseman for $35,000. At the time of his death, Agganis was spending his off-season at his alma mater as an assistant coach, tutoring Tom Gastall, another quarterback who adecided to play professional baseball and died young. Following his 1953 college graduation, Agganis played with Triple-A Louisville where he hit.281 with 23 home runs and 108 RBI. He made his major league debut on April 13, 1954, he had a modest rookie campaign, although he did lead American League first basemen in assists and fielding percentage.
He hit 11 home runs that year, with a. 251 batting average. In 1955, Agganis lost his starting position to rookie Norm Zauchin but regained his spot not long afterwards. On June 2, he was hospitalized with pneumonia after complaining of severe chest pains. Though he rejoined the Red Sox ten days and played two games against the Chicago White Sox, he fell ill again in Kansas City on June 5, he was diagnosed with a viral infection and was flown back to Sancta Maria Hospital in Cambridge, where the doctor on duty stated that Agganis played too soon after his first illness, the reason for the second. The Red Sox placed him on the voluntary retired list until he recuperated, an early version of the disabled list, he began showing signs of improvement, but suffered a fatal pulmonary embolism on June 27, 1955. Baseball was in a state of shock upon hearing of Agganis' death. Red Sox general manager Joe Cronin told the Associated Press that everyone related to the Red Sox organization was "grieved and shocked", saying that Agganis was a "grand boy", while stating that the team would be wearing #6 black armbands to honor Agganis.
American League president Will Harridge commented that his office was "saddened and shocked" by Agganis' death, while Red Sox owner Tom Yawkey stated that he was "stunned," calling Agganis a "man of great character". Ten thousand mourners attended his wake, where his body lay in state at St. George's Greek Orthodox Church in his home city of Lynn. Agganis was inducted into the College Football Hall of Fame in 1974. Gaffney Street, near the former site of Braves Field in Boston, was renamed Harry Agganis Way in 1995. Agganis Arena is a multipurpose sports facility at Boston University; the Harry Agganis Stadium located on Camp Lejeune was named in his honor. The Agganis Foundation has awarded more than $1.1 million in college scholarships to 780 student-athletes from Boston and the North Shore, including Lynn. Scholarships are awarded for athletic achievement; the Foundation was started in 1955 by the Boston Red Sox and owner Thomas A. Yawkey, the Daily Item newspaper and Harold O. Zimman, a mentor of Agganis for whom the football field at Tufts University is named.
Boston University athletics List of baseball players who died during their careers Harry Agganis at the College Football Hall of Fame Career statistics and player information from Baseball-Reference, or Fangraphs, or Baseball-Reference Agganis Arena page