HackerVectors | Chapter 1, Essence of linear algebra
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Further reading 2
How far is next-token prediction from answering a person? →Separate three questions: how an input becomes a representation, how training changes a network and how a capable text predictor becomes an assistant. An explanation at one level does not settle the others.This video helps answer · What is geometric about a word embedding?What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · What do the numbers in a vector describe?
Caption notes
Vectors can be arrows, coordinate lists or abstract objects. Addition and scalar multiplication connect geometric movement to numerical operations.
Original passages · 5
Every pair of numbers gives you one and only one vectorvector addition in this list of numbers conception looks like matching up their termsmultiplying a given vector by a scalar means multiplying each one of those componentsthe ability to translate back and forth between themthere are three distinct but related ideas about vectors