Question

Define orthogonal vector space.

Answer 1

Vector Space and OrthogonalTransform. Definition: A vector space is a set with two operations of addition and scalar multiplication defined for its members, referred to as vectors. ... Existence of zero: there is avector such that: .

Vector Space and Orthogonal 

Answer 2

Answer:

Two vectors are orthogonal if the angle between them is 90 degrees. If two vectors are orthogonal, they form a right triangle whose hypotenuse is the sum of the vectors. Thus, we can use the Pythagorean theorem to prove that the dot product xTy = yT x is zero exactly when x and y are orthogonal.