#### 5.1.1 Vectors

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Dot product

- [E] What’s the geometric interpretation of the dot product of two vectors?
- [E] Given a vector , find vector of unit length such that the dot product of and is maximum.

Outer product

- [E] Given two vectors and . Calculate the outer product ?
- [M] Give an example of how the outer product can be useful in ML.

[E] What does it mean for two vectors to be linearly independent?

- [M] Given two sets of vectors and . How do you check that they share the same basis?
- [M] Given vectors, each of dimensions. What is the dimension of their span?
- Norms and metrics
- [E] What's a norm? What is ?
- [M] How do norm and metric differ? Given a norm, make a metric. Given a metric, can we make a norm?