Metamath Proof Explorer

Table of Contents - 18.3. Normed complex vector spaces

1. Definition and basic properties
   1. cnv
   2. cpv
   3. cba
   4. cns
   5. cn0v
   6. cnsb
   7. cnmcv
   8. cims
   9. df-nv
   10. nvss
   11. nvvcop
   12. df-va
   13. df-ba
   14. df-sm
   15. df-0v
   16. df-vs
   17. df-nmcv
   18. df-ims
   19. nvrel
   20. vafval
   21. bafval
   22. smfval
   23. 0vfval
   24. nmcvfval
   25. nvop2
   26. nvvop
   27. isnvlem
   28. nvex
   29. isnv
   30. isnvi
   31. nvi
   32. nvvc
   33. nvablo
   34. nvgrp
   35. nvgf
   36. nvsf
   37. nvgcl
   38. nvcom
   39. nvass
   40. nvadd32
   41. nvrcan
   42. nvadd4
   43. nvscl
   44. nvsid
   45. nvsass
   46. nvscom
   47. nvdi
   48. nvdir
   49. nv2
   50. vsfval
   51. nvzcl
   52. nv0rid
   53. nv0lid
   54. nv0
   55. nvsz
   56. nvinv
   57. nvinvfval
   58. nvm
   59. nvmval
   60. nvmval2
   61. nvmfval
   62. nvmf
   63. nvmcl
   64. nvnnncan1
   65. nvmdi
   66. nvnegneg
   67. nvmul0or
   68. nvrinv
   69. nvlinv
   70. nvpncan2
   71. nvpncan
   72. nvaddsub
   73. nvnpcan
   74. nvaddsub4
   75. nvmeq0
   76. nvmid
   77. nvf
   78. nvcl
   79. nvcli
   80. nvs
   81. nvsge0
   82. nvm1
   83. nvdif
   84. nvpi
   85. nvz0
   86. nvz
   87. nvtri
   88. nvmtri
   89. nvabs
   90. nvge0
   91. nvgt0
   92. nv1
   93. nvop
2. Examples of normed complex vector spaces
   1. cnnv
   2. cnnvg
   3. cnnvba
   4. cnnvs
   5. cnnvnm
   6. cnnvm
   7. elimnv
   8. elimnvu
3. Induced metric of a normed complex vector space
   1. imsval
   2. imsdval
   3. imsdval2
   4. nvnd
   5. imsdf
   6. imsmetlem
   7. imsmet
   8. imsxmet
   9. cnims
   10. vacn
   11. nmcvcn
   12. nmcnc
   13. smcnlem
   14. smcn
   15. vmcn
4. Inner product
   1. cdip
   2. df-dip
   3. dipfval
   4. ipval
   5. ipval2lem2
   6. ipval2lem3
   7. ipval2lem4
   8. ipval2
   9. 4ipval2
   10. ipval3
   11. ipidsq
   12. ipnm
   13. dipcl
   14. ipf
   15. dipcj
   16. ipipcj
   17. diporthcom
   18. dip0r
   19. dip0l
   20. ipz
   21. dipcn
5. Subspaces
   1. css
   2. df-ssp
   3. sspval
   4. isssp
   5. sspid
   6. sspnv
   7. sspba
   8. sspg
   9. sspgval
   10. ssps
   11. sspsval
   12. sspmlem
   13. sspmval
   14. sspm
   15. sspz
   16. sspn
   17. sspnval
   18. sspimsval
   19. sspims