:: MATRIXR1 semantic presentation
theorem Th1: :: MATRIXR1:1
theorem Th2: :: MATRIXR1:2
theorem Th3: :: MATRIXR1:3
theorem Th4: :: MATRIXR1:4
theorem Th5: :: MATRIXR1:5
theorem Th6: :: MATRIXR1:6
theorem Th7: :: MATRIXR1:7
theorem Th8: :: MATRIXR1:8
theorem Th9: :: MATRIXR1:9
theorem Th10: :: MATRIXR1:10
theorem Th11: :: MATRIXR1:11
theorem Th12: :: MATRIXR1:12
theorem Th13: :: MATRIXR1:13
theorem Th14: :: MATRIXR1:14
theorem Th15: :: MATRIXR1:15
theorem Th16: :: MATRIXR1:16
theorem Th17: :: MATRIXR1:17
theorem Th18: :: MATRIXR1:18
theorem Th19: :: MATRIXR1:19
theorem Th20: :: MATRIXR1:20
theorem Th21: :: MATRIXR1:21
theorem Th22: :: MATRIXR1:22
:: deftheorem Def1 defines MXR2MXF MATRIXR1:def 1 :
:: deftheorem Def2 defines MXF2MXR MATRIXR1:def 2 :
theorem Th23: :: MATRIXR1:23
for b
1, b
2 being
set for b
3 being
Matrix of b
1for b
4 being
Matrix of b
2 holds
( b
3 = b
4 implies for b
5, b
6 being
Nat holds
(
[b5,b6] in Indices b
3 implies b
3 * b
5,b
6 = b
4 * b
5,b
6 ) )
theorem Th24: :: MATRIXR1:24
:: deftheorem Def3 defines + MATRIXR1:def 3 :
theorem Th25: :: MATRIXR1:25
theorem Th26: :: MATRIXR1:26
:: deftheorem Def4 defines - MATRIXR1:def 4 :
:: deftheorem Def5 defines - MATRIXR1:def 5 :
:: deftheorem Def6 defines * MATRIXR1:def 6 :
:: deftheorem Def7 defines * MATRIXR1:def 7 :
theorem Th27: :: MATRIXR1:27
theorem Th28: :: MATRIXR1:28
theorem Th29: :: MATRIXR1:29
theorem Th30: :: MATRIXR1:30
theorem Th31: :: MATRIXR1:31
theorem Th32: :: MATRIXR1:32
theorem Th33: :: MATRIXR1:33
theorem Th34: :: MATRIXR1:34
:: deftheorem Def8 defines 0_Rmatrix MATRIXR1:def 8 :
theorem Th35: :: MATRIXR1:35
theorem Th36: :: MATRIXR1:36
theorem Th37: :: MATRIXR1:37
theorem Th38: :: MATRIXR1:38
theorem Th39: :: MATRIXR1:39
theorem Th40: :: MATRIXR1:40
theorem Th41: :: MATRIXR1:41
theorem Th42: :: MATRIXR1:42
theorem Th43: :: MATRIXR1:43
theorem Th44: :: MATRIXR1:44
:: deftheorem Def9 defines ColVec2Mx MATRIXR1:def 9 :
theorem Th45: :: MATRIXR1:45
theorem Th46: :: MATRIXR1:46
theorem Th47: :: MATRIXR1:47
:: deftheorem Def10 defines LineVec2Mx MATRIXR1:def 10 :
theorem Th48: :: MATRIXR1:48
theorem Th49: :: MATRIXR1:49
theorem Th50: :: MATRIXR1:50
theorem Th51: :: MATRIXR1:51
:: deftheorem Def11 defines * MATRIXR1:def 11 :
:: deftheorem Def12 defines * MATRIXR1:def 12 :
theorem Th52: :: MATRIXR1:52
theorem Th53: :: MATRIXR1:53
theorem Th54: :: MATRIXR1:54
theorem Th55: :: MATRIXR1:55
theorem Th56: :: MATRIXR1:56
theorem Th57: :: MATRIXR1:57
theorem Th58: :: MATRIXR1:58
theorem Th59: :: MATRIXR1:59
theorem Th60: :: MATRIXR1:60
theorem Th61: :: MATRIXR1:61
theorem Th62: :: MATRIXR1:62
theorem Th63: :: MATRIXR1:63
theorem Th64: :: MATRIXR1:64
theorem Th65: :: MATRIXR1:65
theorem Th66: :: MATRIXR1:66