Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tensor multiplication

  1. Nov 20, 2011 #1
    This book says that if [itex]W^aX_a=0[/itex] and [itex]X_a[/itex] is arbitrary, then I should be able to prove that [itex]W^a=0[/itex]. I don't see how this is possible. This is the equivalent of the vector dot product, so if, say, [itex]X_a=(1,0,0,0)[/itex], then [itex]W^a[/itex] could be (0,1,1,1), and the dot product would be [itex]1*0+0*1+0*1+0*1=0[/itex]. Why would [itex]W^a[/itex] have to be 0?
  2. jcsd
  3. Nov 20, 2011 #2


    User Avatar
    Homework Helper

    It means for any Xa not for some Xa. So in your vector example the only vector orthogonal to all vectors is the zero vector.
  4. Nov 21, 2011 #3


    User Avatar
    Science Advisor

    If [itex]X_\alpha[/itex] can be any vector, it can be [itex]W_\alpha[/itex]. If [itex]W^\alpha X_\alpha= 0[/itex] for [itex]X+_\alpha[/itex] any vector then [itex]W^\alpha W_\alpha= 0[/itex] which immediately gives [itex]W^\alpha= 0[/itex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook