??? ???? ??????
	???? ?? ??? ?? ???? ???? ?????? ?? ????? ??????, ???? ?????, ??????? ???? ??????. ??? ???? ???? ?? ?????? ???? ??????? ???? ?????? ?????? ??????? ???? ???? ????? ??????? ???????? ? ????? ?????? . ?? ??? ?????? ?? ???? ????? ?? ??????, ???? ????? ??? ? ?? ????? .

? ?????? ???????? , ??????? ??????? ??? ??????? ??????? ?? ???? ????? ?????? ??? ??? ??????? ???????? , ?????? ?? ????? ${\displaystyle UU^{*}=U^{*}U=I}$, ???? ${\displaystyle U^{*}}$ ??? ? ???? ??????? ?? ${\displaystyle U}$ ?- ${\displaystyle I}$ ??? ??????? ????? . ????? ????, ?????? ??????? ?????? ${\displaystyle A}$ ??? ???????? ?? ${\displaystyle AA^{*}=I}$, ???? ${\displaystyle A^{*}}$ ??? ????? ?????? ?? ??????? ???????? ${\displaystyle A^{t}}$ (??????? ???????, ?? ?????? ?? ??????? ???????? ${\displaystyle \mathbb {C} ^{n}\rightarrow \mathbb {C} ^{n}}$, ???? ? ????? ??????? ????????? ?? ???? ?????????) ?- ${\displaystyle I}$ ??? ?????? ?????? . ??????? ??????? ?????? ??????? ???? ????? ????? ? ???? ?????? ??? 1, ???? ???? ???? ??? ???? ??????? ???????? ????? ?" ???? ?????? ", ????? ??? ???? ????? ${\displaystyle z}$ ????? ?????? ??? 1 ?????: ${\displaystyle z{\bar {z}}=1}$.

????? ????? [ ????? ??? ???? | ????? ]

??? ${\displaystyle V}$ ???? ?????? ????? ???? ??? ??? ??????? ???????? ?? ????? ??????.

${\displaystyle f:V\rightarrow V}$ ???? ??????? ??????? ?? ??????:

${\displaystyle \langle f(u),f(v)\rangle =\langle u,v\rangle }$ ??? ${\displaystyle u,v}$ ?- ${\displaystyle V}$.

????? ???? [ ????? ??? ???? | ????? ]

??????? ??????? ???? ?? ????????? ?? ?????. ??? ???? ???? ???? ?? ???????, ????? ?? ?? ???????. ????? ?? ??????? ???? ???? (?????, ?????? ${\displaystyle \|U(x)\|=\|x\|}$ ??? ${\displaystyle x}$) ??? ???????. ?????? ??????? ???????? ??????? ??? ????? ?? ????? ?? ?????, ????? ???? ?? ?????? ?? ???? ??????????? ??? ???? (???, ?????? ????? ??? ?????? ???????????? ??? ????????). ????, ??????? ?? ?????? ???????? ????? ???? ???????????.

? ?????? ???????? ??????? ??????? ????? ????? ?????? ?? ???? ??????, ???? ?? ??? ????? ???????? ???? ????? ??? ????????.

????? ???????? ?????????? [ ????? ??? ???? | ????? ]

???? ???????? ?????????? ??? ????? ???? ? ??? ??????? . ? ????????? ??? ??????????? ?? ?????? ??? ?? ?????? ${\displaystyle S^{1}}$ ?? ?????? ??????? ???? ??? ????? 1. ? ????? ??? ???? ???????? ?????????? ????? ????????? 1, ??????? ??????? ????????? ??????? .

??????? ??? ?? ?????? ??? ? ???? ???? ? ????? ???????? . ? ???????? ???? ???? ? ???? ??-?? ???? ????? ????? ?? ? ???????? ??????? ??????? ????? ???????? ${\displaystyle SU(3)}$.

???? ??????? ??????? ????? [ ????? ??? ???? | ????? ]

?????? ????? ???????? ??? ?????? ??????????? ; ??????? ?? ?????? ??? ????? ???? ??????????? , ??? ?? ?????? ???.

?? ${\displaystyle A}$ ??????? ?????? ??? ${\displaystyle U=\exp {(iA)}}$ ??? ??????? ???????, ??? ??????? ??????? ??? ??? ???? ???.

??? ?? [ ????? ??? ???? | ????? ]

• ????? SU
• ???????
• ??????
• ??? ??????? ????????
• ?????? ????????
• ???? ??????
• ????? ?????

??????? ???????? [ ????? ??? ???? | ????? ]

• ??????? ??????? , ???? MathWorld (???????)