Linear algebra Linear algebra A 3D projection is a mathematical transformation used to project three dimensional points onto a two dimensional plane. Often this is done to simulate the relationship of the camera to subject. 3D projection is often the first step in the process of representing three dimensional shapes two dimensionally in computer graphics, a process known as rendering. ...more on Wikipedia about "3D projection"
In mathematics and computer science, the adjacency matrix for a finite graph on n vertices is an n × n matrix where the nondiagonal entry aij is the number of edges joining vertex and vertex , and the diagonal entry aii is either twice the number of loops at vertex or just the number of loops (usages differ; this article follows the former; directed graphs always follow the latter). There exists a unique adjacency matrix for each graph, and it is not the adjacency matrix of any other graph. In the special case of a finite, simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected, the adjacency matrix is symmetric. ...more on Wikipedia about "Adjacency matrix"
In linear algebra, the adjugate or classical adjoint of a square matrix is a matrix which plays a role similar to the inverse of a matrix; it can however be defined for any square matrix without the need to perform any divisions. ...more on Wikipedia about "Adjugate matrix"
In mathematics, an affine space is an abstract structure that generalises the affine-geometric properties of Euclidean space. In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one cannot add points, since there is no origin. One-dimensional affine space is the affine line. ...more on Wikipedia about "Affine space"
In geometry, an affine transformation or affine map (from the Latin, affinis, "connected with") between two vector spaces consists of a linear transformation followed by a translation: ...more on Wikipedia about "Affine transformation"
In mathematics, a mapping f : V → W from a complex vector space to another is said to be antilinear (or conjugate-linear or semilinear) if ...more on Wikipedia about "Antilinear map"
In linear algebra, the augmented matrix of a matrix is obtained by appending a column to it, typically to the right. ...more on Wikipedia about "Augmented matrix"
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In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K with an absolute value |.|) is a set S so that for all scalars α with |α| ≤ 1 ...more on Wikipedia about "Balanced set"
In mathematics, barycentric coordinates are coordinates defined by the vertices of a simplex. Barycentric coordinates are a form of homogeneous coordinates. ...more on Wikipedia about "Barycentric coordinates (mathematics)"
In linear algebra, a basis is a minimum set of vectors that, when combined, can address every vector in a given space. More precisely, a basis of a vector space is a set of linearly independent vectors that span the whole space. ...more on Wikipedia about "Basis (linear algebra)"
A bicomplex number is a number written in the form, a + bi1 + ci2 + dj, where i1, i2 and j are imaginary units. Based on the rules for multiplying the imaginary units, then if A = a + bi1 and B = c + di1, then the bicomplex number may be written A + Bi2. Thus, bicomplex numbers are similar to complex numbers, but the two parts are complex rather than real. Bicomplex numbers reduce to complex numbers when A and B are real numbers. ...more on Wikipedia about "Bicomplex number"
A bidiagonal matrix is a symmetric tridiagonal matrix, a special type of matrix representation from the LAPACK Fortran package. ...more on Wikipedia about "Bidiagonal matrix"
In mathematics, the notion of canonical basis refers to a basis of an algebraic structure which is canonical in a sense that depends on the precise context: ...more on Wikipedia about "Canonical basis"
In mathematics, Vect(K, Z/2Z) denotes the category whose objects are "all" of the Z/2Z- graded vector spaces over the given field K. The morphisms of this category are given by the even and odd linear transformations between any two such objects. A linear transformation φ: A → B is said to be even if it maps the even part ([0] mod 2) of A to the even part of B and the odd part ([1] mod 2) of A to the odd part of B, and is said to be odd if it maps the even part of A to the odd part of B and the odd part of A to the even part of B. Note that any linear transformation can the expressed uniquely as the sum of an even and an odd linear transformation. ...more on Wikipedia about "Category of graded vector spaces"
In mathematics, especially category theory, the category K-Vect has all vector spaces over a fixed field K as objects and linear transformations as morphisms. If K is real, then the category is known as Vec. ...more on Wikipedia about "Category of vector spaces"
In linear algebra, the Cauchy-Binet formula generalizes the multiplicativity of the determinant (the fact that the determinant of a product of two square matrices is equal to the product of the two determinants) to non-square matrices. ...more on Wikipedia about "Cauchy-Binet formula"
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field, satisfies its own characteristic equation. ...more on Wikipedia about "Cayley–Hamilton theorem"
The change of bases describes the process of converting elements in one basis to another when both describe the same elements of the finite field GF(pm). ...more on Wikipedia about "Change of bases"
In linear algebra, the characteristic equation of a square matrix A is the equation in one variable λ ...more on Wikipedia about "Characteristic equation"
In linear algebra, one associates a polynomial to every square matrix, its characteristic polynomial or secular equation. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace. ...more on Wikipedia about "Characteristic polynomial"
In linear algebra, a column vector is an m × 1 matrix, i.e. a matrix consisting of a single column. ...more on Wikipedia about "Column vector"
In mathematics, one associates to every complex vector space V its complex conjugate vector space V*, again a complex vector space. ...more on Wikipedia about "Complex conjugate vector space"
A matrix in mathematics is conformable, if its dimensions are suitable for some operation (addition, multiplication, etc.). In order to be conformable to addition, matrices need to have the same dimension, so that in ...more on Wikipedia about "Conformable"
In mathematics, the conjugate transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A* obtained from A by taking the transpose and then taking the complex conjugate of each entry. Formally ...more on Wikipedia about "Conjugate transpose"
In mathematics, specifically in linear algebra, the coordinate space, Fn, is the prototypical example of an n-dimensional vector space over a field F. ...more on Wikipedia about "Coordinate space"
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