In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. The method is named after Carl Friedrich Gauss (1777–1855), although it was known to Chinese mathematicians as early as 179 A.D..
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally.
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Its name is alleged to be derived from the fictitious drug soma consumed as a pastime by the establishment in Aldous Huxley's dystopic novel Brave New World.
In linear algebra, a symmetric
real matrix
is said to be positive definite if the scalar
is strictly positive for every non-zero column vector
of
real numbers. Here
denotes the transpose of
.. When interpreting
as the output of an operator,
, that is acting on an input,
, the property of positive definiteness implies that the output always has a positive inner product with the input, as often observed in physical processes.
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. Less frequently, some mathematics books use U or E to represent the identity matrix, meaning "unit matrix" and the German word "Einheitsmatrix", respectively.
A crossword is a word puzzle that usually takes the form of a square or a rectangular grid of white-and black-shaded squares. The game's goal is to fill the white squares with letters, forming words or phrases, by solving clues, which lead to the answers. In languages that are written left-to-right, the answer words and phrases are placed in the grid from left to right and from top to bottom. The shaded squares are used to separate the words or phrases.
A logic puzzle is a puzzle deriving from the mathematics field of deduction.
The Animatrix is a 2003 American–Japanese animated science fiction anthology film produced by the Wachowskis. It is a compilation of nine animated short films based on The Matrix trilogy, which was written and directed by the Wachowskis. Four of the shorts were also written by the Wachowskis. The film details the backstory of the Matrix universe, including the original war between man and machines which led to the creation of the titular Matrix.
In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero. By contrast, if most of the elements are nonzero, then the matrix is considered dense. The number of zero-valued elements divided by the total number of elements is called the sparsity of the matrix. Using those definitions, a matrix will be sparse when its sparsity is greater than 0.5.
Count Zero is a science fiction novel by American-Canadian writer William Gibson, originally published in 1986. It is the second volume of the Sprawl trilogy, which begins with Neuromancer and concludes with Mona Lisa Overdrive, and is an example of the cyberpunk subgenre.
Stratigraphy is a key concept to modern archaeological theory and practice. Modern excavation techniques are based on stratigraphic principles. The concept derives from the geological use of the idea that sedimentation takes place according to uniform principles.
When archaeological finds are below the surface of the ground, the identification of the context of each find is vital in enabling the archaeologist to draw conclusions about the site and about the nature and date of its occupation. It is the archaeologist's role to attempt to discover what contexts exist and how they came to be created. Archaeological stratification or sequence is the dynamic superimposition of single units of stratigraphy, or contexts.
In mathematics, particularly matrix theory, a band matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it. More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an eigenvector of T if T(v) is a scalar multiple of v. This condition can be written as the equation
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. LU decomposition was introduced by mathematician Tadeusz Banachiewicz in 1938.
In numerical linear algebra, an incomplete LU factorization of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.
Picross DS (ピクロスDS) is a puzzle video game developed by Jupiter and published by Nintendo for the Nintendo DS handheld video game console. It is the second Picross game to be released by Nintendo in Europe and North America after Mario's Picross suffered a commercial failure in regions outside Japan, where many Picross games have been released for several Nintendo consoles. Like other Picross games, it presents the player with a series of nonogram logic puzzles to solve. It was first released in Japan, and was later released in North America, Europe and Australia.
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 × 3, because there are two rows and three columns:
Wordplay is a game show presented by Jenny Powell and sometimes Jenni Falconer. It aired live weekdays from 23 March to 31 July 2009 on Channel 5 and was axed after only one series.
Zero Escape, formerly released in Japan as Kyokugen Dasshutsu , is a series of adventure games directed and written by Kotaro Uchikoshi. The first two entries in the series, Nine Hours, Nine Persons, Nine Doors (2009) and Zero Escape: Virtue's Last Reward (2012), were developed by Spike Chunsoft, while the third entry, Zero Time Dilemma (2016), was developed by Chime. Zero Escape is published by Spike Chunsoft in Japan, while Aksys Games and Rising Star Games have published the games for North America and Europe respectively.
