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invertible system

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  • Invertible matrix — In linear algebra an n by n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n by n matrix B such that where In denotes the n by n identity matrix and the multiplication used is ordinary… …   Wikipedia

  • Linear system of divisors — A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of… …   Wikipedia

  • Root system — This article discusses root systems in mathematics. For root systems of plants, see root. Lie groups …   Wikipedia

  • Non-invertible — Matrice inversible En mathématiques et plus particulièrement en algèbre linéaire, une matrice carrée A d ordre n est dite inversible ou régulière ou encore non singulière, s il existe une matrice B d ordre n telle que AB = BA = In, ( AB = In… …   Wikipédia en Français

  • Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… …   Wikipedia

  • Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

  • Gaussian elimination — In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It 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… …   Wikipedia

  • Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… …   Wikipedia

  • Cramer's rule — In linear algebra, Cramer s rule is a theorem, which gives an expression for the solution of a system of linear equations with as many equations as unknowns, valid in those cases where there is a unique solution. The solution is expressed in… …   Wikipedia

  • Hill cipher — Hill s cipher machine, from figure 4 of the patent In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was… …   Wikipedia

  • Applications of Multiple Coordinate Systems — The application of multiple coordinate systems is an effective tool in control systems. The usage of multiple coordinate systems can improve the efficiency of calculations as well as enhance clarity in operations. Mathematically, coordinate… …   Wikipedia

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