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In convex optimization, a linear matrix inequality (LMI) is an expression of the form ():= + + + + where = [, =, …,] is a real vector,,,, …, are symmetric matrices, is a generalized inequality meaning is a positive semidefinite matrix belonging to the positive semidefinite cone + in the subspace of symmetric matrices .
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
Download as PDF; Printable version ... In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It ...
Download as PDF; Printable version; ... In mathematics a linear inequality is an inequality which involves a linear function. ... where A is an m×n matrix, ...
Finsler's lemma can be used to give novel linear matrix inequality (LMI) characterizations to stability and control problems. [4] The set of LMIs stemmed from this procedure yields less conservative results when applied to control problems where the system matrices has dependence on a parameter, such as robust control problems and control of ...
In mathematics, there are many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices. [1] [2] [3] [4]
If A or B is a multiple of the identity matrix, then this criterion is also necessary. The Loewner order does not have the least-upper-bound property, and therefore does not form a lattice. It is bounded: for any finite set of matrices, one can find an "upper-bound" matrix A that is greater than all of S. However, there will be multiple upper ...
Korn's theorem is a quantitative version of this statement, which intuitively says that if the gradient of a vector field is on average not far from the space of skew-symmetric matrices, then the gradient must not be far from a particular skew-symmetric matrix. The statement that Korn's inequality generalizes thus arises as a special case of ...