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Bra-ket notation and other linear algebra stuff

  1. Jan 16, 2014 #1
    forgive the messiness; i take bad notes in class.

    http://i.imgur.com/VmW8Ubg.jpg

    towards the middle of the page where it says "this is equivalent to..." and then my professor wrote what follows but i thought the row vector should be complex conjugates? ie, the red writings are not actually part of the notes, i just wrote them because i was confused as to why they weren't there.



    http://i.imgur.com/5zGGBe3.jpg

    towards the bottom right, where it has a(hermitian)IbI, which are all matrices by the way, i don't understand where the second 'I' (unit matrix) came from (where i stated my confusion in the notes).


    btw, does anyone know how to shrink an image when i do ['img']link['/img']? sometimes these images are too large
     
  2. jcsd
  3. Jan 16, 2014 #2
    Your first remark is correct. They should be complex conjugates.

    For the second part if you have numbers like [tex]a\cdot u^{-1} \cdot u \cdot b[/tex].
    Than you get [tex]a\cdot 1\cdot b[/tex]. you can freely multiply this entire expression with 1.

    I believe the second unit matrix is added to convert the vector b in the transposed vector b since otherwise you have the product of 2 column vectors.
     
  4. Jan 18, 2014 #3
    towards the bottom of the page where i wrote "where'd this one come from?", to the RHS of that, i have 'ab'.

    but if this is to become < a | b > , then shouldn't the 'a' in 'ab' be hermitian?
     
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