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