Geometry and algebra of linear maps, vectors, and matrices
You often need to store a category in a computer: a color, an animal, a day of the week. The easy trick is to number them, red is 0, blue is 1, green is 2, but that number is only an address. Category 2 is not twice category 1 the way the number 6 really is twice the number 3, and there's no real sense in which blue sits "between" red and green.
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