 Control 1 / Primavera 2012, Matrices - Geometría |
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Foro fmat.cl > Programa Enseñanza Universitaria > Comunidades Universitarias > Universidad de Chile > Álgebra Lineal  |
 Sep 9 2012, 09:29 PM
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#11
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 Dios Matemático  Grupo: Usuario FMAT Mensajes: 277 Registrado: 15-October 08 Desde: Santiagopolis Miembro Nº: 36.209 Nacionalidad:  Colegio/Liceo:  Universidad:  Sexo:   |
Una duda nada que ver, cómo le dicen sus pruebas, "certamenes", "pruebas", "interrogaciones"?
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Sep 9 2012, 09:32 PM
Publicado:
#12
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 Maestro Matemático Grupo: Usuario FMAT Mensajes: 81 Registrado: 10-October 11 Miembro Nº: 95.494 Universidad:  |
CITA(Kamufler @ Sep 9 2012, 09:29 PM)  Una duda nada que ver, cómo le dicen sus pruebas, "certamenes", "pruebas", "interrogaciones"? ''control'' |
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Sep 11 2012, 12:45 PM
Publicado:
#13
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Maestro Matemático Grupo: Usuario FMAT Mensajes: 113 Registrado: 17-May 08 Miembro Nº: 23.481 Nacionalidad: Colegio/Liceo:  Universidad: Sexo: |
CITA(Shine @ Sep 3 2012, 10:12 AM) Semestre beta es el segundo semestre Semestre alfa es el primer semestre Según tengo entendido le dicen semestre beta, a cuando das el ramo en un semestre que no corresponde por malla.. Ej ahora por malla corresponde dar cálculo diferencial y álgebra lineal, entonces esos ramos son en semestre alfa, pero quienes lo den el próximo semestre lo darán en semestre beta |
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Sep 22 2012, 04:33 PM
Publicado:
#14
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 Dios Matemático Supremo Grupo: Usuario FMAT Mensajes: 560 Registrado: 24-December 09 Miembro Nº: 64.629 |
CITA(Uchiha Itachi @ Sep 1 2012, 06:25 PM) ![TEX: % MathType!MTEF!2!1!+-<br />% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaqjEa<br />% qaaiaadofacaWGqbGaaGOmaaaaaeaacaWGHbGaaiykaiaabsfacaqG<br />% YbGaaeyyaiaabkgacaqGHbGaaeOAaiaabggacaqGUbGaaeizaiaab+<br />% gacaqGGaGaae4yaiaab+gacaqGUbGaaeiiaiaabcfacaqG6aaabaGa<br />% amiuamaaCaaaleqabaGaaGOmaaaakiabg2da9maabmaabaGaamysai<br />% abgkHiTiaad2eadaqadaqaaiaad2eadaahaaWcbeqaaiaadshaaaGc<br />% caWGnbaacaGLOaGaayzkaaWaaWbaaSqabeaacqGHsislcaaIXaaaaO<br />% GaamytamaaCaaaleqabaGaamiDaaaaaOGaayjkaiaawMcaamaabmaa<br />% baGaamysaiabgkHiTiaad2eadaqadaqaaiaad2eadaahaaWcbeqaai<br />% aadshaaaGccaWGnbaacaGLOaGaayzkaaWaaWbaaSqabeaacqGHsisl<br />% 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6aGaaeiiaiaadcfacaWGnbGaeyypa0ZaaiWaaeaacaWGjbGaeyOeI0<br />% IaamytamaabmaabaGaamytamaaCaaaleqabaGaamiDaaaakiaad2ea<br />% aiaawIcacaGLPaaadaahaaWcbeqaaiabgkHiTiaaigdaaaGccaWGnb<br />% WaaWbaaSqabeaacaWG0baaaaGccaGL7bGaayzFaaGaamytaiabg2da<br />% 9iaad2eacqGHsislcaWGnbWaaeWaaeaacaWGnbWaaWbaaSqabeaaca<br />% WG0baaaOGaamytaaGaayjkaiaawMcaamaaCaaaleqabaGaeyOeI0Ia<br />% aGymaaaakiaad2eadaahaaWcbeqaaiaadshaaaGccaWGnbGaeyypa0<br />% JaamytaiabgkHiTiaad2eacqGH9aqpcaaIWaaabaaabaGaeyO0H4Ta<br />% amiuaiaad2eacqGH9aqpcaaIWaaabaaabaGaamOyaiaacMcacaqGGa<br />% WaaeWaaeaacaWGnbWaaWbaaSqabeaacaWG0baaaOGaamytaaGaayjk<br />% aiaawMcaamaaCaaaleqabaGaamiDaaaakiabg2da9iaad2eadaahaa<br />% WcbeqaaiaadshaaaGccaWGnbGaaeiiaiaabYcacaqGGaGaaeiBaiaa<br />% bwhacaqGLbGaae4zaiaab+gacaqGGaGaamytamaaCaaaleqabaGaam<br />% iDaaaakiaad2eacaqGGaGaaeyzaiaabohacaqGGaGaae4CaiaabMga<br />% caqGTbGaaeyzaiaabshacaqGYbGaaeyAaiaabogacaqGHbGaaeOlaa<br />% qaaiabgkziUkaadcfadaahaaWcbeqaaiaadshaaaGccqGH9aqpdaqa<br />% daqaaiaadMeacqGHsislcaWGnbWaaeWaaeaacaWGnbWaaWbaaSqabe<br />% aacaWG0baaaOGaamytaaGaayjkaiaawMcaamaaCaaaleqabaGaeyOe<br />% I0IaaGymaaaakiaad2eadaahaaWcbeqaaiaadshaaaaakiaawIcaca<br />% GLPaaadaahaaWcbeqaaiaadshaaaGccqGH9aqpcaWGjbGaeyOeI0Ya<br />% aeWaaeaacaWGnbWaaeWaaeaacaWGnbWaaWbaaSqabeaacaWG0baaaO<br />% GaamytaaGaayjkaiaawMcaamaaCaaaleqabaGaeyOeI0IaaGymaaaa<br />% kiaad2eadaahaaWcbeqaaiaadshaaaaakiaawIcacaGLPaaadaahaa<br />% WcbeqaaiaadshaaaGccqGH9aqpcaWGjbGaeyOeI0Iaamytamaadmaa<br />% baWaaeWaaeaacaWGnbWaaWbaaSqabeaacaWG0baaaOGaamytaaGaay<br />% jkaiaawMcaamaaCaaaleqabaGaeyOeI0IaaGymaaaaaOGaay5waiaa<br />% w2faamaaCaaaleqabaGaamiDaaaakiaad2eadaahaaWcbeqaaiaads<br />% haaaaakeaacqGH9aqpcaWGjbGaeyOeI0IaamytamaabmaabaGaamyt<br />% amaaCaaaleqabaGaamiDaaaakiaad2eaaiaawIcacaGLPaaadaahaa<br />% WcbeqaaiabgkHiTiaaigdaaaGccaWGnbWaaWbaaSqabeaacaWG0baa<br />% aOGaeyypa0JaamiuaaqaaaqaaiaabYeacaqG1bGaaeyzaiaabEgaca<br />% qGVbGaaeilaiaabccacaqGqbGaaeiiaiaabwgacaqGZbGaaeiiaiaa<br />% bohacaqGPbGaaeyBaiaabwgacaqG0bGaaeOCaiaabMgacaqGJbGaae<br />% yyaiaab6caaaaa!7CF7!<br />\[<br />\begin{gathered}<br /> \boxed{SP2} \hfill \\<br /> a){\text{Trabajando con P:}} \hfill \\<br /> P^2 = \left( {I - M\left( {M^t M} \right)^{ - 1} M^t } \right)\left( {I - M\left( {M^t M} \right)^{ - 1} M^t } \right) \hfill \\<br /> = I - 2\left( {M\left( {M^t M} \right)^{ - 1} M^t } \right) + \left( {M\left( {M^t M} \right)^{ - 1} M^t } \right)\left( {M\left( {M^t M} \right)^{ - 1} M^t } \right) \hfill \\<br /> = I - 2\left( {M\left( {M^t M} \right)^{ - 1} M^t } \right) + M\left( {M^t M} \right)^{ - 1} \left( {M^t M} \right)\left( {M^t M} \right)^{ - 1} M^t \hfill \\<br /> = I - 2\left( {M\left( {M^t M} \right)^{ - 1} M^t } \right) + M\left( {M^t M} \right)^{ - 1} M^t \hfill \\<br /> = I - \left( {M\left( {M^t M} \right)^{ - 1} M^t } \right) = P \hfill \\<br /> \hfill \\<br /> \Rightarrow P^2 = P \hfill \\<br /> \hfill \\<br /> {\text{Y a su vez: }}PM = \left\{ {I - M\left( {M^t M} \right)^{ - 1} M^t } \right\}M = M - M\left( {M^t M} \right)^{ - 1} M^t M = M - M = 0 \hfill \\<br /> \hfill \\<br /> \Rightarrow PM = 0 \hfill \\<br /> \hfill \\<br /> b){\text{ }}\left( {M^t M} \right)^t = M^t M{\text{ }}{\text{, luego }}M^t M{\text{ es simetrica}}{\text{.}} \hfill \\<br /> \to P^t = \left( {I - M\left( {M^t M} \right)^{ - 1} M^t } \right)^t = I - \left( {M\left( {M^t M} \right)^{ - 1} M^t } \right)^t = I - M\left[ {\left( {M^t M} \right)^{ - 1} } \right]^t M^t \hfill \\<br /> = I - M\left( {M^t M} \right)^{ - 1} M^t = P \hfill \\<br /> \hfill \\<br /> {\text{Luego}}{\text{, P es simetrica}}{\text{.}} \hfill \\ <br />\end{gathered} <br />\]](/tex-image/70c4a02a9bde86d84057570f000711fa.png) de que manera transpusiste?? se supone que  y yo veo que haces 
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