References: What vectors actually are

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Linear Algebra, Chapter 1: "Vectors, what even are they?"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/vectors
  Series index: https://www.3blue1brown.com/?topic=linear-algebra
  License: copyright Grant Sanderson; videos published on his site and YouTube
Clawdemy's lessons are original prose that follows the pedagogical arc of this
series. We do not reproduce or transcribe the videos; we cite them as the
recommended companion. All rights to the original videos remain with the creator.

Watch this next

• Vectors, what even are they? (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors, on the creator’s own site. Where the lesson keeps the arrows still on the page, Sanderson animates them: you watch addition happen tip to tail and watch scaling stretch an arrow in real time. About ten minutes, no prerequisites beyond what you have here. If the geometric picture felt abstract in text, this is the fastest way to make it move.

Going deeper

A short, durable list. Each link is a specific next step, not a generic pile.

• Essence of Linear Algebra (full series) by 3Blue1Brown. The series this track follows. Chapter 2, “Linear combinations, span, and basis vectors”, is the natural next watch and maps to the next lesson in this track. The series is the gold standard for geometric intuition in linear algebra.

• Khan Academy: Vectors for a slower, exercise-driven walk through the same ground. If you learn best by doing many small problems with immediate feedback, start here alongside the videos.

• Linguistic Regularities in Continuous Space Word Representations (Mikolov et al., 2013). The paper that introduced the king-man+woman analogy and the broader linguistic-regularities framing for early word embeddings. If you want to see exactly what those early embeddings could and could not do, this is the primary source for the example in the “Why this matters when you use AI” section.

Adjacent topics

Where this leads inside this track.

• Linear combinations, span, and basis vectors. The next lesson. Once you can add and scale vectors, the natural question is: starting from a few vectors, which points can you reach by adding and scaling them? That set is the span, and it is built entirely from the two operations you learned here.

• Linear transformations and matrices. A few lessons ahead. A matrix turns out to be a rule for moving every vector in space at once, and “what a 2x2 matrix does to the unit square” becomes a thing you can sketch. It rests directly on the arrow-and-coordinate bridge introduced in this lesson.