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Math Help - Bilinear/Linear Maps

  1. #1
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    Bilinear/Linear Maps

    Hi
    I don't understand why addition is a linear map but not a bilinear map, and on the other hand why multiplication is a bilinear map but not a linear one.

    Can someone please tell me why this is the case?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Alex314 View Post
    Hi
    I don't understand why addition is a linear map but not a bilinear map, and on the other hand why multiplication is a bilinear map but not a linear one.

    Can someone please tell me why this is the case?
    T(x,y)=x+y.

    T(x+z,y_0)=x+z+y_0\ne T(x,y_0)+T(z,y_0)=x+z+y+z.

    L(x,y)=xy

    L(x+z,y_0)=(x+z)y_0=xy_0+zy_0=L(x,y+0)+L(z,y_0)
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