Grassmann's Identity

Theorem
Let $K$ be a division ring.

Let $\struct {G, +_G, \circ}_K$ be a $K$-vector space.

Let $M$ and $N$ be finite-dimensional subspaces of $G$.

Then the sum $M + N$ and intersection $M \cap N$ are finite-dimensional, and:
 * $\map \dim {M + N} + \map \dim {M \cap N} = \map \dim M + \map \dim N$

Also known as
This result can also be referred to as Grassmann's formula.