Элементы теории симметрии. Часть I. Кирсанов А.А. - 3 стр.

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3
Ñîäåðæàíèå
Ïðåäèñëîâèå .................................................................................... 7
Ãëàâà I. Ëèíåéíûå ïðîñòðàíñòâà
§1.1. Ëèíåéíîå ïðîñòðàíñòâî .................................................................. 9
§1.2. Ïðèìåðû ëèíåéíûõ ïðîñòðàíñòâ. ................................................ 11
§1.3. Ýëåìåíòàðíûå ñëåäñòâèÿ èç àêñèîì ëèíåéíîãî
ïðîñòðàíñòâà ................................................................................. 15
§1.4. Ëèíåéíàÿ çàâèñèìîñòü .................................................................. 17
§1.5. Êîíå÷íîìåðíûå è áåñêîíå÷íîìåðíûå ïðîñòðàíñòâà.
Áàçèñ .......................................................................................... 17
§1.6. Èçîìîðôèçì ëèíåéíûõ ïðîñòðàíñòâ ........................................... 21
§1.7. Ñîîòâåòñòâèå ìåæäó êîìïëåêñíûìè è äåéñòâèòåëüíûìè
ïðîñòðàíñòâàìè ............................................................................ 22
§1.8. Ëèíåéíîå ïîäïðîñòðàíñòâî ......................................................... 24
§1.9. Ñêàëÿðíîå ïðîèçâåäåíèå .............................................................. 24
§1.10. Êîìïëåêñíûå åâêëèäîâû ïðîñòðàíñòâà ...................................... 30
1.10.1. Îáùèå îïðåäåëåíèÿ ......................................................... 30
1.10.2. Èçîìîðôèçì êîìïëåêñíûõ åâêëèäîâûõ
ïðîñòðàíñòâ ..................................................................... 33
1.10.3. Àíòèèçîìîðôèçì ïðîñòðàíñòâ ....................................... 34
1.10.4. Ãèëüáåðòîâî ïðîñòðàíñòâî ............................................. 34
§1.11. Ëèíåéíûå îïåðàòîðû .................................................................... 35
§1.12. Äåéñòâèÿ íàä îïåðàòîðàìè .......................................................... 38
§1.13. Ñîïðÿæåííûé îïåðàòîð ............................................................... 41
§ 1.14. Óíèòàðíûé îïåðàòîð ................................................................... 44
§ 1.15. Ýðìèòîâ îïåðàòîð ........................................................................ 45
§ 1.16. Ïðîåêòèðóþùèé îïåðàòîð .......................................................... 46
§1.17. Ïðîèçâîëüíûé ëèíåéíûé îïåðàòîð â êîìïëåêñíîì
åâêëèäîâîì ïðîñòðàíñòâå ............................................................ 47
Ãëàâà II. Êîíñòðóêöèè íàä ïðîñòðàíñòâàìè è îïåðàòîðàìè
§2.1. Äóàëüíûå ïðîñòðàíñòâà ............................................................... 49
§2.2. Äóàëüíûå áàçèñû .......................................................................... 54
§2.3. Äóàëüíûå îïåðàòîðû .................................................................... 55
                                                                                                         3




                                        Ñîäåðæàíèå
        Ïðåäèñëîâèå .................................................................................... 7
        Ãëàâà I. Ëèíåéíûå ïðîñòðàíñòâà
§1.1. Ëèíåéíîå ïðîñòðàíñòâî .................................................................. 9
§1.2. Ïðèìåðû ëèíåéíûõ ïðîñòðàíñòâ. ................................................ 11
§1.3. Ýëåìåíòàðíûå ñëåäñòâèÿ èç àêñèîì ëèíåéíîãî
        ïðîñòðàíñòâà ................................................................................. 15
§1.4. Ëèíåéíàÿ çàâèñèìîñòü .................................................................. 17
§1.5. Êîíå÷íîìåðíûå è áåñêîíå÷íîìåðíûå ïðîñòðàíñòâà.
        Áàçèñ .......................................................................................... 17
§1.6. Èçîìîðôèçì ëèíåéíûõ ïðîñòðàíñòâ ........................................... 21
§1.7. Ñîîòâåòñòâèå ìåæäó êîìïëåêñíûìè è äåéñòâèòåëüíûìè
        ïðîñòðàíñòâàìè ............................................................................ 22
§1.8. Ëèíåéíîå ïîäïðîñòðàíñòâî ......................................................... 24
§1.9. Ñêàëÿðíîå ïðîèçâåäåíèå .............................................................. 24
§1.10. Êîìïëåêñíûå åâêëèäîâû ïðîñòðàíñòâà ...................................... 30
        1.10.1. Îáùèå îïðåäåëåíèÿ ......................................................... 30
        1.10.2. Èçîìîðôèçì êîìïëåêñíûõ åâêëèäîâûõ
                ïðîñòðàíñòâ ..................................................................... 33
        1.10.3. Àíòèèçîìîðôèçì ïðîñòðàíñòâ ....................................... 34
        1.10.4. Ãèëüáåðòîâî ïðîñòðàíñòâî ............................................. 34
§1.11. Ëèíåéíûå îïåðàòîðû .................................................................... 35
§1.12. Äåéñòâèÿ íàä îïåðàòîðàìè .......................................................... 38
§1.13. Ñîïðÿæåííûé îïåðàòîð ............................................................... 41
§ 1.14. Óíèòàðíûé îïåðàòîð ................................................................... 44
§ 1.15. Ýðìèòîâ îïåðàòîð ........................................................................ 45
§ 1.16. Ïðîåêòèðóþùèé îïåðàòîð .......................................................... 46
§1.17. Ïðîèçâîëüíûé ëèíåéíûé îïåðàòîð â êîìïëåêñíîì
        åâêëèäîâîì ïðîñòðàíñòâå ............................................................ 47

      Ãëàâà II. Êîíñòðóêöèè íàä ïðîñòðàíñòâàìè è îïåðàòîðàìè
§2.1. Äóàëüíûå ïðîñòðàíñòâà ............................................................... 49
§2.2. Äóàëüíûå áàçèñû .......................................................................... 54
§2.3. Äóàëüíûå îïåðàòîðû .................................................................... 55

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