Having the equation a T x = bwhere a, a , x ∈ R n , b is a number. Can I solve x in terms of a, b?Ultimate goal is to find the maximum of 1 2 x T P xgiven a T x = b, where P is a symmetric positive definite matrix.

Question

Having the equation      a    T    x  =  bwhere   a,  a  ,  x  ∈            R        n  ,   b is a number. Can I solve   x in terms of   a,  b?Ultimate goal is to find the maximum of      1    2        x    T    P  xgiven       a    T    x  =  b, where   P is a symmetric positive definite matrix.

1c2ru3x · Accepted Answer

Solve first order conditions for the Lagrangian problem, then optimal could be calculated.

Brooke Kramer · Accepted Answer

This maximization problem is equivalent to maximizing the norm of   x with respect to the inner product induced by   P on             R        n  .On the other hand, given   a and   b the equation       a          T        x  =  b defines an affine plane on             R        n  , so generally there should be no such maximum, ie, the value of       1    2        x    T    P  x should be unbounded on that plane.

Having the equation a T </msup> x = b where a , a ,

Answered question

Answer & Explanation

New Questions in High school geometry