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# Inner Products

## What and why

Inner products are operations that take 2 vectors $$\vec{x}, \vec{y}$$ in the vector space $$V$$ as inputs and return a scalar. We denote the inner product using angle brackets: $$\langle \vec{x}, \vec{y} \rangle$$

$$\langle \vec{x}, \vec{y}\rangle: V \times V \rightarrow \mathbb{R}$$

Inner products can be used to compare two vectors in the vector space and are helpful in finding the projection of a vector onto the a vector subspace.

**Quick overview of inner products:**

{% embed url="<https://youtu.be/LyGKycYT2v0>" %}