Desigualdades determinantes para matrices definidas positivas a través de desigualdades young aditivas y multiplicativas
Publicado 2022-12-09
Palabras clave
- Matrices definidas positivas,
- Determinantes,
- Desigualdades
Cómo citar
Derechos de autor 2022 Revista Integración, temas de matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Resumen
En este trabajo demostramos entre otros que, si las matrices definidas positivas A, B de orden n satisface la condición < mIn ≤ B −A ≤ M In, para algunas constantes 0 < m < M, donde In es la matriz identidad, entonces
0 ≤ (1 − t) [det (A)]−1 + t [det (A + mIn)]−1 − [det (A + mtIn)]−1
≤ (1 − t) [det (A)]−1 + t [det (B)]−1 − [det ((1 − t) A + tB)]−1
≤ (1 − t) [det (A)]−1 + t [det (A + M In)]−1 − [det (A + M tIn)]−1,
para todo t ∈ [0, 1].
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Referencias
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