Do I understand sigma notation correctly?

Question

Mathematics

Yes:





Question: please explain how L_2 will look like for, for example, some:
Y^ =
Y =

PS perhaps I even wrote the sets incorrectly, so if anything, please correct it

PSS and in general, it is desirable to explain what the index (?) and degree (?) after ||. And did I understand correctly that a double module is the norm ?

Thank you very much in advance

Answer 1

Yyou have from the set R^W*H*2. Those. Y consists of W*H*2numbers indexed by three indices - the first one is up to w, the second one is up to h, the third one is up to 2. Accordingly, the sum of all values ​​of the first two indices is calculated in the formula. Y_whis a pair of numbers. Your sets in the example are incorrectly composed - instead of a and b there should be pairs of numbers.
Next, subscript 2 after || - this is the notation for the L2 norm in two-dimensional space - this is the second root of the sum of squares (the usual Cartesian distance). Superscript after || is just a squaring that overrides the rooting for ||...||_2.
Those. This whole formula says to take the W*H*2 componentwise differences, square them, and add them up.