# Bilinear/Linear Maps

• March 30th 2010, 01:12 PM
Alex314
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?
• March 30th 2010, 02:30 PM
Drexel28
Quote:

Originally Posted by Alex314
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?

$T(x,y)=x+y$.

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

$L(x,y)=xy$

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