Explore: Matrix Inequalities

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

"A survey on Cauchy–Bunyakovsky–Schwarz type discrete inequalities", Journal of Inequalities in Pure and Applied Mathematics, 4 (3): 142 pp, archived

Algebra, Part II (1975, Marcel Dekker), and A Survey of Matrix Theory and Matrix Inequalities (1st edition 1964; reprint 1969; Dover reprint 1992). In

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

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

inequalities. Aequationes Mathematicae 40 (1990) 89–93. Liu, Shuangzhe and Neudecker, Heinz, A survey of Cauchy-Schwarz and Kantorovich-type matrix inequalities

Markov's inequality or Chebyshev's inequality. The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's

ISBN 0-486-66434-1. Marcus, Marvin; Minc, Henryk (1992). A survey of matrix theory and matrix inequalities. Dover Publications. p. 81. ISBN 0-486-67102-X. Norman,

section). For matrix A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} of rank r {\displaystyle r} , the following inequalities hold: ‖ A ‖ 2

is no need to define linear inequalities using those signs. A system of linear inequalities is a set of linear inequalities in the same variables: a 11