<Dl> <Dd> 0 → V → V →...→ V → 0 </Dd> </Dl> <Dd> 0 → V → V →...→ V → 0 </Dd> <P> is an exact sequence of finite - dimensional vector spaces, then </P> <Dl> <Dd> ∑ i = 1 r (− 1) i dim ⁡ (V i) = 0 . (\ displaystyle \ sum _ (i = 1) ^ (r) (- 1) ^ (i) \ dim (V_ (i)) = 0 .) </Dd> </Dl>

The sum of the rank and the nullity of a matrix is equal to the number of rows of the matrix