:: Some Properties Of Some Special Matrices, Part {II}
:: by Xiaopeng Yue , Dahai Hu , Xiquan Liang and Zhongpin Sun
::
:: Received January 4, 2006
:: Copyright (c) 2006 Association of Mizar Users
:: deftheorem Def1 defines Idempotent MATRIX_8:def 1 :
:: deftheorem Def2 defines Nilpotent MATRIX_8:def 2 :
:: deftheorem Def3 defines Involutory MATRIX_8:def 3 :
:: deftheorem Def4 defines Self_Reversible MATRIX_8:def 4 :
theorem Th1: :: MATRIX_8:1
theorem Th2: :: MATRIX_8:2
theorem :: MATRIX_8:3
theorem :: MATRIX_8:4
theorem :: MATRIX_8:5
theorem :: MATRIX_8:6
theorem :: MATRIX_8:7
theorem :: MATRIX_8:8
theorem :: MATRIX_8:9
theorem Th10: :: MATRIX_8:10
theorem :: MATRIX_8:11
theorem :: MATRIX_8:12
theorem :: MATRIX_8:13
theorem :: MATRIX_8:14
theorem :: MATRIX_8:15
theorem :: MATRIX_8:16
theorem :: MATRIX_8:17
theorem :: MATRIX_8:18
theorem :: MATRIX_8:19
theorem :: MATRIX_8:20
theorem :: MATRIX_8:21
theorem :: MATRIX_8:22
theorem :: MATRIX_8:23
theorem :: MATRIX_8:24
theorem :: MATRIX_8:25
theorem :: MATRIX_8:26
theorem :: MATRIX_8:27
theorem Th28: :: MATRIX_8:28
theorem :: MATRIX_8:29
theorem :: MATRIX_8:30
theorem :: MATRIX_8:31
theorem :: MATRIX_8:32
theorem :: MATRIX_8:33
:: deftheorem Def5 defines is_similar_to MATRIX_8:def 5 :
theorem :: MATRIX_8:34
theorem :: MATRIX_8:35
theorem :: MATRIX_8:36
theorem :: MATRIX_8:37
theorem :: MATRIX_8:38
theorem :: MATRIX_8:39
theorem :: MATRIX_8:40
theorem :: MATRIX_8:41
theorem :: MATRIX_8:42
theorem :: MATRIX_8:43
:: deftheorem Def6 defines is_congruent_Matrix_of MATRIX_8:def 6 :
theorem :: MATRIX_8:44
canceled;
theorem :: MATRIX_8:45
theorem :: MATRIX_8:46
theorem :: MATRIX_8:47
theorem :: MATRIX_8:48
theorem :: MATRIX_8:49
theorem :: MATRIX_8:50
theorem :: MATRIX_8:51
theorem :: MATRIX_8:52
:: deftheorem defines Trace MATRIX_8:def 7 :
theorem :: MATRIX_8:53
theorem Th54: :: MATRIX_8:54
theorem :: MATRIX_8:55
theorem Th56: :: MATRIX_8:56
theorem Th57: :: MATRIX_8:57
theorem :: MATRIX_8:58
theorem :: MATRIX_8:59
theorem Th60: :: MATRIX_8:60
theorem :: MATRIX_8:61
theorem :: MATRIX_8:62
theorem :: MATRIX_8:63