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.


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