For vectors u, v in a complex inner product space, we have
if and only if

.

Question

For vectors u, v in a complex inner product space, we have 
  if and only if 
  
.

Quizplus · Accepted Answer

This is a standard result in complex inner product spaces, known as the Cauchy-Schwarz inequality. It states that the inner product of two vectors (in this case u and v) is bounded by the product of their norms, i.e., |<u,v>| <= ||u||*||v||. The equality holds if and only if one vector is a scalar multiple of the other, which is precisely the condition given in the statement.

For Vectors U, V in a Complex Inner Product Space