Vectors
What a vector is from three directions at once — a list of numbers, an arrow in space, and a thing you can add and scale.
This lesson is part of a preview roadmap.
The engine around it is real — progress, notes and bookmarks all work — but the video has not been through the sourcing and review protocol a shipped lesson goes through. See the roadmap for what that means.
Vectors
The player loads from youtube-nocookie.com when you press play. Nothing reaches YouTube before that.
What you'll learn
- A vector has three equally valid readings — a list, an arrow, and an element of a space where addition and scaling are defined.
- Addition is tip-to-tail; scaling stretches or flips without changing direction.
- Coordinates are not the vector; they are the vector written down in one particular basis.
Why this is the first node
Everything downstream of here — a layer of a network, a token embedding, an attention head — is a vector operation wearing a different name. Starting anywhere else means learning each of those as a separate trick instead of as one idea applied three times.
What to watch for
The video spends its first minutes on something that looks like a detour: three different communities each think “vector” means a different thing. It is not a detour. The physics reading (an arrow with magnitude and direction), the data reading (an ordered list of numbers), and the algebraic reading (anything you can add and scale) are the three views you will keep switching between, and the switch is usually where confusion starts.
Where this sits
The next node turns two vectors into a single number, which is the operation a neural network performs more often than any other. Nothing here requires calculus yet — that arrives in its own node and the two meet at gradient descent.
Check yourself
Why does it matter that a vector can be read as a list and as an arrow?
Because every later idea borrows one reading or the other — data is lists, geometry is arrows, and linear algebra is the dictionary between them.
What changes about a vector when you change basis?
Its coordinates change; the vector itself does not. The arrow stays where it is while the ruler you measure it with moves.
Go deeper
The maths underneath
Notes
Notes are saved to your account.
Everything else on this page works without one — progress and bookmarks keep themselves in this browser and come with you when you sign in. Notes are the one thing worth not trusting to a browser you might clear.
Your notes could not be loaded.