Vectors

What is it?

Formulas

$$\norm{v} = \sqrt{v_1^2 + \dots + v_n^2}$$

Euclidean norm (length)

Where it shows up in computing

• Physics engines★★★★★fundamentalPhysics and simulation

  Positions, velocities and forces are 3D vectors updated every frame.

Where it shows up in AI

• Neural networks★★★★★fundamentalAI and machine learning

  Inputs, activations and parameters are vectors (and tensors) in $\R^n$.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

What depends on it

• Dot product
• Matrices and linear maps
• Functions of several variables
• Gradient
• Vector fields
• Curvature (basic differential geometry)