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Kernel


For any function f:A->B (where A and B are any sets), the kernel (also called the null space) is defined by

 Ker(f)={x:x in Asuch thatf(x)=0},

so the kernel gives the elements from the original set that are mapped to zero by the function. Ker(f) is therefore a subset of A

The related image of a function is defined by

 Im(f)={f(x):x in A}.

Im(f) is therefore a subset of B.


See also

Image, Ker, Null Space, Rank-Nullity Theorem

Portions of this entry contributed by Rahmi Jackson

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Cite this as:

Jackson, Rahmi and Weisstein, Eric W. "Kernel." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kernel.html

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