In convex optimization, a linear matrix inequality (LMI) is an expression of the form LMI ⁡ ( y ) := A 0 + y 1 A 1 + y 2 A 2 + ⋯ + y m A m ⪰ 0 {\displaystyle...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: < less than...

geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality. Alternatively, the set of n × n positive semidefinite matrices...

In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It can be used to estimate...

satisfying the triangle inequality) The only feature distinguishing matrices from rearranged vectors is multiplication. Matrix norms are particularly useful...

v {\displaystyle \mathbf {v} } are linearly dependent. Sedrakyan's inequality, also known as Bergström's inequality, Engel's form, Titu's lemma (or the...

lengths of these vectors ||vi||. Specifically, Hadamard's inequality states that if N is the matrix having columns vi, then | det ( N ) | ≤ ∏ i = 1 n ‖ v...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

International, a media-company in the United States of America Linear matrix inequality Linux Mark Institute Lisp Machines, Inc. Lista Monumentelor Istorice...

used, particularly in results related to robust optimization and linear matrix inequalities. Let x ∈ Rn, and Q ∈ Rn x n and L ∈ Rn x n be symmetric matrices...

Kantorovich, a pioneer in the field of linear programming. There is also Matrix version of the Kantorovich inequality due to Marshall and Olkin (1990). Its...

formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints...

with one state, the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems, and conservation laws can often be...

equation in stability theory. It establishes a relation between a linear matrix inequality involving the state space constructs A, B, C and a condition in...

general linear group under matrix multiplication, i.e. the following matrices are unimodular: Identity matrix The inverse of a unimodular matrix The product...

of a linear space with a basis. Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group...

European control conference (ECC). IEEE, 2001. Boyd, Stephen, et al. Linear matrix inequalities in system and control theory. Vol. 15. Siam, 1994. Advances in...

In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first...

many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with...

Pages 371–418. Stephen Boyd and Lieven Vandenberghe Convex Optimization, Cambridge University Press, 2004, p.655. Linear matrix inequality Finsler's lemma...

form a subgroup of the general linear group G L ( 2 n ; R ) {\displaystyle \mathrm {GL} (2n;\mathbb {R} )} under matrix multiplication since being symplectic...

0,} i.e., a second-order cone constraint is equivalent to a linear matrix inequality. The nomenclature here can be confusing; here M ≽ 0 {\displaystyle...

matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the linear...

In mathematics, and in particular linear algebra, the Moore–Penrose inverse ⁠ A + {\displaystyle A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called...

0,} meaning that the matrix H + L ( α ) {\displaystyle H+L(\alpha )} is positive-semidefinite. This is a linear matrix inequality (LMI) feasibility test...

particular skew-symmetric matrix. The statement that Korn's inequality generalizes thus arises as a special case of rigidity. In (linear) elasticity theory,...

homogeneous linear parametric equations, the span of a collection of vectors, and the null space, column space, and row space of a matrix. Geometrically...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices....