#### 5.1.1 Vectors

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1. Dot product

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

1. [E] Given two vectors and . Calculate the outer product ?
2. [M] Give an example of how the outer product can be useful in ML.
3. [E] What does it mean for two vectors to be linearly independent?

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