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Math Help - Matrix of a Composite

  1. #1
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    Matrix of a Composite

    f(x) = Ax
    g(x) = Bx

    First we do the f and then the g, which is written g 0 f. So the final matrix is BA. So why is the first matrix transformation written and done last?
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  2. #2
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    Quote Originally Posted by mark090480 View Post
    f(x) = Ax
    g(x) = Bx

    First we do the f and then the g, which is written g 0 f. So the final matrix is BA. So why is the first matrix transformation written and done last?
    Because BA operates on whatever is to the right of it.
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    I'm not sure if I understand. Can you explain a bit more?
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    f(x) means that the function f is applied to the number x that is to its right. g(f(x)) means that g is applied to f(x), to its right. Ax means the matrix A is multiplied by the vector x to its right. BAx means that the matrix B is multiplied by the vector Ax to its right. If f(x)= Ax and g(x)= Bx then g(f(x))= g(Ax)= B(Ax)= BAx.
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    Thanks, It was easier than I thought.
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  6. #6
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    Quote Originally Posted by mark090480 View Post
    f(x) = Ax
    g(x) = Bx

    First we do the f and then the g, which is written g 0 f. So the final matrix is BA. So why is the first matrix transformation written and done last?
    Because (g \circ f)(x) means g(f(x))=g(Ax)=B(Ax)=BAx

    CB
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