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Mathematics of Machine Learning
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Representing multiple measurements as a tuple (x1,x2,…,xn) is a natural idea that has a ton of merits. The tuple form suggests that the components belong together in a precise order, giving a clear and concise way to store information.
However, this comes at a cost: now we have to work with more complex objects. Despite dealing with tuples like (x1,…,xn) instead of numbers, there are similarities. For instance, any two tuple x = (x1,…,xn) and y = (y1,…,yn)
It’s almost like using a number.
These operations have clear geometric interpretations as well. Addition is the same as translation, while multiplication with a scalar is a simple stretching. (Or squeezing, if |c|<1.)
On the other hand...