# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 72: Bilinear Maps

In linear algebra, a bilinear map is a function $f: X \times Y \rightarrow Z$, where $X, Y, Z$ are vector spaces over a common field, which is linear in each of its 2 components when the other is held fixed. When $f(x, y) = f(y, x)$ for all $(x, y) \in X \times Y$, it is referred to as a symmetric bilinear map.

Examples of bilinear maps include matrix multiplication, the inner product, and the cross product.