Gramian matrix
[ˈɡreɪmiən ˈmeɪtrɪks]
nounpl: Gramian matrices
matriz de Gram
1. A square matrix constructed from a set of vectors, where each element is the inner product of two vectors in the set. Used in linear algebra to determine linear independence and orthogonality.
The Gramian matrix of the vectors v1 and v2 is computed by taking the inner products of all pairs of vectors.
A matriz de Gram dos vetores v1 e v2 é computada calculando os produtos internos de todos os pares de vetores.
2. In control theory, a matrix used to analyze the controllability or observability of a linear system.
The controllability Gramian matrix helps determine if a linear system can be controlled by its inputs.
A matriz de Gram de controlabilidade ajuda a determinar se um sistema linear pode ser controlado por suas entradas.
The term 'Gramian matrix' is primarily used in academic and technical contexts within mathematics, engineering, and control theory. It is named after Jørgen Pedersen Gram, a Danish mathematician. This is specialized terminology not commonly encountered in everyday language in either Brazil, Portugal, or the USA, but is standard in universities and research settings worldwide.
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