CODEWITHSUNDEEP
math
john
john

Reputation: 39

What does this expression mean?

I'm writing a small application about image retrieval, but I can't understand what this mathematical expression means

d^2 = || x - p ||^2 where x and p are two-element vectors.

Can somebody tell me what means this ||, and how can I raise a vector to power ??

EDIT Thanks to espertus answer I know that || x - p ||^2 is a euclidean distance. However I also came across this expression ||p||^2 . What would that mean ? I think that it can't be euclidean distance. What else could it be ?

Upvotes: 0

Views: 1106

Answers (2)

duffymo
duffymo

Reputation: 308743

"EDIT Thanks to espertus answer I know that || x - p ||^2 is a euclidean distance. However I also came across this expression ||p||^2 . What would that mean ? I think that it can't be euclidean distance. What else could it be ?"

It would be the magnitude of the vector p. If p is expressed in terms of its terminus coordinates (x, y) or (x, y, z), then ||p|| is the distance from the origin (0, 0) or (0, 0, 0) to the terminus.

Upvotes: 0

Ellen Spertus
Ellen Spertus

Reputation: 6805

The two bars refer to the length of a vector, which is the square root of the sum of the squares of the coordinates. See http://en.wikipedia.org/wiki/Euclidean_vector#Length.

Upvotes: 5

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