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UBA - CienciaS • Ver Tema - Primer Recuperatorio del Segundo Parcial - 17/12/08
UBACS Q&A Foro WikiCS
Fecha actual 27 Jun 2022, 02:05

Todos los horarios son UTC - 3 horas




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 Asunto: Primer Recuperatorio del Segundo Parcial - 17/12/08
NotaPublicado: 31 Dic 2008, 17:58 
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Registrado: 16 May 2008, 22:21
Mensajes: 194
Ubicación: Pilar, Bs. As.
Enunciados:

1. Sean ,
, .
Hallar tal que .

2. (a) Hallar todas las posibles formas de Jordan de una matriz tal que y .
(b) Hallar todas las posibles formas de Jordan de una matriz tal que divide a y .

3. Sea matrices hermitianas y sea : definida por .

(a) Probar que es autoadjunta para el producto interno definido por .
(b) Probar que si es un autovector de y es un autovector de , entonces es un autovector de .
(c) Hallar una base ortonormal de formada por autovectores de , si y . Calcular la matriz de en esa base.

4. Sean el plano .

(a) Hallar un plano alabeado con y que esté a distancia de .
(b) Sea un plano cualquiera que satisface lo pedido en (a) y sean y los subespacios asociados a y a . Probar que .

5. Sea : una forma bilineal simétrica cuya matriz en la base canónica de es . Sea : definida por . Probar que la signatura de es el doble de la de .


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Todos los horarios son UTC - 3 horas


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