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Inner product generated by matrix

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Find d(u, v), where the inner product is defined by the matrix

    [1 2]
    [-1 3]

    and u = (-1, 2), v = (2, 5)

    2. Relevant equations

    <u, v> = Au . Av
    d(u, v) = abs(u - v)

    3. The attempt at a solution

    I first tried to find the resulting inner product from the matrix in terms of an equation:

    I got it to be:

    2u1v1 + 13u2v2

    Then I simply found u - v, which came to be (-3, -3)

    And thus d(u, v) = <-3, -3>0.5

    This, in terms of the relevant inner product, is:

    [2(9) + 13(9)]0.5

    Unfortunately, the books answer does not agree? It says it is 3 times root 13. I get root 135?
  2. jcsd
  3. Sep 28, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Check your inner product calculation. There should be some u1v2 and u2v1 terms
  4. Sep 28, 2011 #3
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