Linear Algebra MOC
Linear algebra studies spaces, vectors, linear maps, bases, and eigenvectors. It is the mathematical layer behind Susskind’s quantum mechanics notes: quantum states are vectors, observables are operators, and measurement uses eigenvalues.
Core local notes
- Vector space — the base structure: add vectors and scale them without leaving the space.
- Hilbert space — physics-facing quantum state space with inner products and normalisation.
- Observable — Hermitian operators as measurable quantities.
Useful route for physics
- Understand linear combinations and bases in Vector space.
- Treat a quantum state as a vector in Hilbert space, not as a tiny object moving through ordinary space.
- Read operators as transformations of vectors; eigenvectors are states with sharp values for an Observable.
- Use noncommutation to understand the Uncertainty principle.
Bridges
- Quantum Mechanics MOC uses the vector-space language directly.
- Hamiltonian mechanics and Poisson bracket show the classical algebra that quantum commutators replace.
- Maths MOC is the parent maths map.
Source trail: Susskind The Theoretical Minimum index; reference book: Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman.