Let and be vector spaces over a field , and let be a linear transformation. Assuming the dimension of is finite, then
where is the dimension of , is the kernel, and is the image.
Note that is called the nullity of and is called the rank of .
Let and be vector spaces over a field , and let be a linear transformation. Assuming the dimension of is finite, then
where is the dimension of , is the kernel, and is the image.
Note that is called the nullity of and is called the rank of .
This entry contributed by Rahmi Jackson
Jackson, Rahmi. "Rank-Nullity Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Rank-NullityTheorem.html