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Matrix multiplication vs dot product

  1. May 21, 2012 #1
    What is the difference between matrix multiplication and the dot product of two matrices? Is there a difference?


    [tex]A =
    a & b \\
    c & d


    [tex]B =
    e & f \\
    g & h

    then does
    {\mathbf{A} \cdot \mathbf{B}} =
    ae & bf \\
    cg & dh


    [tex]AB =
    ae + bg & af + bh \\
    ce + dg & cf + dh

    ? Is this correct? Any help would be appreciated.
  2. jcsd
  3. May 21, 2012 #2


    User Avatar
    Gold Member

    Don't confuse dot product of matrix with vectors. The second product is correct.
  4. May 21, 2012 #3

    [tex]{\mathbf{A} \cdot \mathbf{B}} = AB =
    ae + bg & af + bh \\
    ce + dg & cf + dh

    With matrices the dot product means that you need to multiply the matrices? Correct?
  5. May 21, 2012 #4
    Usually the "dot product" of two matrices is not defined. I think a "dot product" should output a real (or complex) number. So one definition of A[itex]\bullet[/itex]B is ae + bf + cg + df. This is thinking of A, B as elements of R^4. If we want our dot product to be a bi-linear map into R this is how we need to define it (up to multiplication by a constant).
  6. May 21, 2012 #5
    You should view AB as a collection of dot products ie.
    ab11 (top left of AB) can be described as the dot product of

    a & b
    e \\

    and so on for the rest of the positions.
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