vector processing

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Technology Connections explains why the superheterodyne radio has its name and how mixing frequencies lets it tune stations well. It walks through the underlying wave phenomena and algebra and why the design solved a hard tuning problem.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.

MinutePhysics explains that computers store brightness nonlinearly, so blurring and blending colors in raw RGB gives wrong, dark results. It shows why mixed colors, such as in gradients, look off.

Pannenkoek explains how Super Mario 64 handles wall, floor and ceiling collisions, including triangles, normal vectors, quarter steps and out of bounds. It is a detailed 37-minute technical walkthrough of the game's physics.

Matt Parker on Numberphile explains the strange properties of spheres in higher dimensions, such as how they poke out of their bounding boxes. It uses Pythagoras to build intuition for 4D and beyond.