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Inner product of rank 2 tensor and a vector

  1. Nov 27, 2012 #1
    I been reading some material that lead me to understand that it takes an inner product of a dyad and a vector to obtain another vector at an angle to the initial one... cross product among two vectors would be an option only if we are willing to settle to a right angle.
    After few days i countered a situation where i see an inner product of a vector and a dyad resulting in a vector of different magnitude but same direction as the earlier one. i mean to say
    [ A*v = η.v ]
    A= a random dyad
    v= a vector
    η= a scalar.

    now the question is, what is the condition for such an interaction ?? what should be the property of such a tensor ?!
  2. jcsd
  3. Nov 27, 2012 #2


    Staff: Mentor

    look at a 2D version of a matrix and a vector say M x V = n x V

    M x V = results in:

    n*vx=m11*vx + m12*vy


    n*vy = m21*vx + m22*vy

    so what could you set the m values to make the two equations true?
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