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(???? ?????? ?? ?????????? ?????? ?? ??? ??? ??
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??? ????????? ???? ????? ??), ????-?????????? ???? (R3) ???? ?? ??????? ???? ??? ?????? (??-?????) ??????? ????? ?? ??? ????? ?????? × ??? ????? ????? ??? ?? ????? ??? '?? ????????
?????
a ??? b ????? ??? ?? ???? ??????? a × b, ??? ????? ????? ????? ?? ????? ??? ???????????? (?????) ????? ?? ??? ?? ?? ?? ????? ??? ???? ???? ???? (????) ??? ????? (90 ????? ??) ????? ??? ?? ????
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???? ???? ?????? ??????????? (?????) ??? ?????
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) ???? ????? ???????
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[
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[1]
[2]
???? ??????? ?? ????? ??????
[
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[note 1]
determinant
:
?? ??????????? ???
?????? ?? ????
?? ???? ???? ??? ??? ???? ?? ???? ?? ???
??????? ??????
?? ???? ??? ?? ??? ???? ?? ???? ??
?????? ???? ???? ????? ???, ?? ?? ?????? ????? ??
??????? ????? ????? ??? ????? ???? ?? ??? ?? ????? ?? ???, ?? ?? ?????? ????? ??
[3]
?? ????? ??????? ?? ????? ????? ?? ?? ????? ??
????????????
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???? ?? ??-????? ??????? ?? ???? ?? ????? ??, ??? ???? ???? ??????? ?? ?? ???? ????? ??:
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a
???
b
?? ????? ?? ?? ??????? ????????
t
???? ????? ???? ???
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[
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???-??????????
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- ↑
Here, “formal" means that this notation has the form of a determinant, but does not strictly adhere to the definition; it is a mnemonic used to remember the expansion of the cross product.
????? ????
[
????
]
- Hazewinkel, Michiel, ed. (2001),
"Cross product"
,
???? ?? ?????????
, ???????,
ISBN
978-1-55608-010-4
- Weisstein, Eric W.
,
???????.html "???? ???????"
,
????-?????
.
- A quick geometrical derivation and interpretation of cross products
- C.A. Gonano and R.E. Zich (2014).
Cross product in N Dimensions - the doublewedge product
, Polytechnic University of Milan, Italy.
- Z.K. Silagadze (2002). Multi-dimensional vector product. Journal of Physics. A35, 4949
Archived
2015-09-05 at the
Wayback Machine
. (it is only possible in 7-D space)
- Real and Complex Products of Complex Numbers
- An interactive tutorial
Archived
2006-04-24 at the
Wayback Machine
. created at
Syracuse University
? (requires
java
)
- W. Kahan (2007). Cross-Products and Rotations in Euclidean 2- and 3-Space. University of California, Berkeley (PDF).