Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
CyberpunkCyberpunk is a subgenre of science fiction in a dystopian futuristic setting that tends to focus on a "combination of lowlife and high tech", featuring futuristic technological and scientific achievements, such as artificial intelligence and cyberware, juxtaposed with societal collapse, dystopia or decay. Much of cyberpunk is rooted in the New Wave science fiction movement of the 1960s and 1970s, when writers like Philip K. Dick, Michael Moorcock, Roger Zelazny, John Brunner, J. G.
UtopiaA utopia (juːˈtoʊpiə ) typically describes an imaginary community or society that possesses highly desirable or near-perfect qualities for its members. It was coined by Sir Thomas More for his 1516 book Utopia, which describes a fictional island society in the New World. It can also refer to an intentional community. Hypothetical utopias focus on, among other things, equality in categories such as economics, government and justice, with the method and structure of proposed implementation varying according to ideology.
Orthogonal matrixIn linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is where QT is the transpose of Q and I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: where Q−1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the Hermitian adjoint (conjugate transpose) of Q, and therefore normal (Q∗Q = QQ∗) over the real numbers.
Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
