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Vectors and Vector Spaces
”I want to point out that the class of abstract linear spaces is no larger than the class of spaces whose elements are arrays. So what is gained by abstraction? First of all, the freedom to use a single symbol for an array; this way we can think of vectors as basic building blocks, unencumbered by components. The abstract view leads to simple, transparent proofs of results.”
— Peter D. Lax, in Chapter 1 of his book Linear Algebra and its Applications
The mathematics of machine learning rests upon three pillars: linear algebra, calculus, and probability theory. Linear algebra describes how to represent and manipulate data; calculus helps us fit the models; while probability theory helps interpret them.
These build on top of each other, and we will start at the beginning: representing and manipulating data.
To guide us throughout this section, we will look at the famous Iris dataset ( https://en.wikipedia.org/wiki/Iris_flower_data_set...
