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Math Help - Multiplying three matrices together

  1. #1
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    Multiplying three matrices together

    How do I do this? Say for example:

    A = [a b] x [e f] x [i j]
    [c d] [g h] [k l]

    Or do I just multiply the first two matrices together to get a 2x2 matrix, then multiply that with the third matrix on the end?
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  2. #2
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    Quote Originally Posted by Denny Crane View Post
    How do I do this? Say for example:

    A = [a b] x [e f] x [i j]
    [c d] [g h] [k l]

    Or do I just multiply the first two matrices together to get a 2x2 matrix, then multiply that with the third matrix on the end?
    Suppose we want to calculate A = XYZ

    Matrix multiplication is associative, so the above statement is unambiguous. We can either calculate

    A = (XY)Z

    or

    A = X(YZ)

    There is a related optimisation problem known as Matrix chain multiplication, which asks which order is the most efficient.
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