matrix inequality
[ˈmeɪtrɪks ɪnɪˈkwɒlɪti]
nounpl: matrix inequalities
desigualdade matricial
1. A mathematical statement comparing two matrices using inequality symbols (≤, ≥, <, >), often in the context of semidefinite programming or linear algebra where matrices are ordered using the Loewner partial order
The matrix inequality A ≤ B means that B - A is a positive semidefinite matrix.
A desigualdade matricial A ≤ B significa que B - A é uma matriz semidefinida positiva.
2. An inequality involving matrix norms or eigenvalues used to establish bounds on matrix properties
The Cauchy-Schwarz matrix inequality provides bounds for inner products of vectors.
A desigualdade matricial de Cauchy-Schwarz fornece limites para produtos internos de vetores.
Matrix inequalities are fundamental concepts in advanced mathematics, optimization, and control theory, predominantly used in academic and engineering contexts in both Brazil and the USA. The terminology is standardized across Portuguese-speaking countries and in international mathematical literature.
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