We know that the the norm of a vector is norm(vec(u))=sqrt(u_1^2+u_2^2+...+u_n^2), where vec(u) in RR^n. How does the d xx 1 vector look like using the definition of norm, and what does RR^n really means? Or what is Rn for the d xx 1 vector?

Kelton Molina 2022-09-22 Answered
We know that the the norm of a vector is u = u 1 2 + u 2 2 + . . . + u n 2 , where u R n . How does the d x 1 vector look like using the definition of norm, and what does R n really means? Or what is R n for the d x 1 vector?
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Answers (1)

Jacey Humphrey
Answered 2022-09-23 Author has 7 answers
It is on the unit sphere.
It might help to work with lower specific number of n, say n = 1 , 2 , 3
If n = 1, then u = 1 or u = 1
If n = 2, then it lies on the unit circle, u 1 2 + u 2 2 = 1
If n = 3, then it lies on the unit circle, u 1 2 + u 2 2 + u 3 2 = 1
R 2 means { ( x , y ) T | x , y R }, similary for general R d
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