4차원 내적의 의미??
JongHoon Ryu
3차원 까지는 직관적으로 이해 하다가도 4차원부터는 완전히 수식적으로
밖에 이해 할 수 없습니다.
어떻게 하면 , 수식이 아닌 "느낌"으로 , 4차원이상에서의 내적의 의미를
알 수 있을까요??
또 , inner product over complex field C 의 의미도 , 1차원 까지는
알겠지만 ,
2차원부터는 , 잘 모르겠습니다.
아래 글은 제가 sci.math 에 위와 같은 질문을 했을때의 답변인데 ,
별 대단한 내용은 없는 것 같습니다.
"JongHoon Ryu" <jhr...@hyowon.pusan.ac.kr> writes:
>i had a problem when i was studying linear algebra.
>what is the intuitive meaning of the multidimentional inner product?
>how can i see the 4 dimentional ( or more ) axes and convince myself
>that i can get the Fourier coefficient just by multiplying each of
>elements of two vectors and dividing them by norm of one ?
I don't know what would count as "intuitive meaning" for you.
But I conclude from your phrasing that you believe you already
have a grasp on the "intuitive meaning" of the 2-dimensional
inner product. In that case, you know all you need to know!
For, given two vectors in a Euclidian space of dimension 3
or more (or a Hilbert space), they always lie in a 2-dimensional
subspace, which inherits a Euclidian structure from the ambient
3-or-more-dimensional space.
Lee Rudolph