设[tex=21.0x1.571]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+hVTIREG04nfnohj3+3XWYMMsCLvUXp2+4cOBBgWP4LysvMw8iTR+PUn0KqP3gq9fOSmalmrjAy2TbvgAD1nFVfy1Oinz9c4/I96aiIxT2k5p5PcIIeMmPdkqaO9G7zrfx95yC2bgGpuwxci2BKvZXOb6bpcPPkfUF3dzpZaymYmgAHn/C/dpEdouePYl46kffeblAoFYNzuvoFeevlKyz0[/tex]其中范数定义为[tex=11.214x4.214]C2Z1okXIB9N6IXD+I3AE30V4KRCMUuCW1s0jlSfvlLWZz/YRFbiOS71BkBeBKBXSDcPweigVYRGZIv3NEorLT+ad2ji6SOyIH7ItbIYfkqYWKZxBxhMaDNv+T1bbrZv6yO1iXIipHBmyfznTq3mrTw==[/tex]又对 [tex=5.929x1.357]IYH/UBb8Awi/yk8qRDzRLeVx3pYuN3TFsZqQrUGoRw/P5J4ReCDovIXN/JqN2sb2ErDA6pQpKcPl9LStH4iw+Q==[/tex]定义[tex=23.929x3.0]WIrYU0rKhL/zpyMF9weCsaT+cNX3DFRVwwrhJk4Ig0pf2BYG9jEnxYL28N2rZKbelVMZWrmYdevd2BzFWmOlQbfgcFRI+gbe4aelp/qhVLdT0WEj+0jaTOu67HCV5qmjKO9DKza8wQy2Fsd+eRSpvbPcVPXHIGqmopVl8Eya5EpeHrPFv5gFvfckpiW6rtKz3hs7dYqyoZM1Ew96fxSLy7srOg2nptL090SOGzbN988hGlEAH24sl4a+8ebX8zTVRi4DmEIph5Cp+kgekoNjNQ==[/tex]求证:(1) [tex=4.143x1.429]WIrYU0rKhL/zpyMF9weCsXVUVnoIJViv50bDvDsbw3U=[/tex](2) [tex=2.429x1.286]TcPYtqbLyx9HEJHO4uMSi/jOa0fUSR2ermpAS6B3lSc=[/tex] 是 [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]的等价模;(3) [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]完备.
设[tex=21.0x1.571]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+hVTIREG04nfnohj3+3XWYMMsCLvUXp2+4cOBBgWP4LysvMw8iTR+PUn0KqP3gq9fOSmalmrjAy2TbvgAD1nFVfy1Oinz9c4/I96aiIxT2k5p5PcIIeMmPdkqaO9G7zrfx95yC2bgGpuwxci2BKvZXOb6bpcPPkfUF3dzpZaymYmgAHn/C/dpEdouePYl46kffeblAoFYNzuvoFeevlKyz0[/tex]其中范数定义为[tex=11.214x4.214]C2Z1okXIB9N6IXD+I3AE30V4KRCMUuCW1s0jlSfvlLWZz/YRFbiOS71BkBeBKBXSDcPweigVYRGZIv3NEorLT+ad2ji6SOyIH7ItbIYfkqYWKZxBxhMaDNv+T1bbrZv6yO1iXIipHBmyfznTq3mrTw==[/tex]又对 [tex=5.929x1.357]IYH/UBb8Awi/yk8qRDzRLeVx3pYuN3TFsZqQrUGoRw/P5J4ReCDovIXN/JqN2sb2ErDA6pQpKcPl9LStH4iw+Q==[/tex]定义[tex=23.929x3.0]WIrYU0rKhL/zpyMF9weCsaT+cNX3DFRVwwrhJk4Ig0pf2BYG9jEnxYL28N2rZKbelVMZWrmYdevd2BzFWmOlQbfgcFRI+gbe4aelp/qhVLdT0WEj+0jaTOu67HCV5qmjKO9DKza8wQy2Fsd+eRSpvbPcVPXHIGqmopVl8Eya5EpeHrPFv5gFvfckpiW6rtKz3hs7dYqyoZM1Ew96fxSLy7srOg2nptL090SOGzbN988hGlEAH24sl4a+8ebX8zTVRi4DmEIph5Cp+kgekoNjNQ==[/tex]求证:(1) [tex=4.143x1.429]WIrYU0rKhL/zpyMF9weCsXVUVnoIJViv50bDvDsbw3U=[/tex](2) [tex=2.429x1.286]TcPYtqbLyx9HEJHO4uMSi/jOa0fUSR2ermpAS6B3lSc=[/tex] 是 [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]的等价模;(3) [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]完备.