A-Gate / Math Concepts
Mathematical Foundations of Quantum EEG Analysis
Progressive curriculum building from linear algebra through differential geometry to quantum computing. Each module has interactive visualizations. Start from the top and work down — each module builds on the previous.
01 — Foundations
01
Eigenvalues & Eigenvectors Foundational
The natural axes of a matrix. Eigenvectors are special directions that don't rotate under transformation; eigenvalues measure how much they stretch.
Interactive 4 Scenes
02
Covariance Matrices Foundational
How EEG channels relate to each other. Each window of brain activity becomes a covariance matrix capturing correlation structure between electrodes.
Prerequisites: Eigenvalues 4 Scenes
03
SPD Matrices Intermediate
Symmetric Positive Definite matrices form a curved manifold. Every valid covariance matrix lives on this manifold. Explore the boundary where matrices become singular.
Prerequisites: Covariance 2 Panels
04
Phase Locking Value Intermediate
Hilbert-transform phase synchrony encoded as quantum rotation angles. The direct bridge between raw EEG and the A-Gate circuit.
Prerequisites: Covariance 4 Scenes
02 — Geometry
05
Riemannian Geometry Intermediate
The SPD manifold is curved, not flat. Geodesics are the shortest paths; tangent spaces let us do linear algebra locally.
Prerequisites: SPD 5 Scenes
06
Bures Manifold Advanced
Quantum density matrices form their own manifold with the Bures metric. The structural identity between SPD and Bures manifolds explains why quantum circuits can read covariance geometry.
Prerequisites: Riemannian 3D Trajectory
03 — Quantum
07
Quantum States Intermediate
Qubits in superposition on the Bloch sphere. Measurement collapses superposition to definite outcomes with specific probabilities.
Prerequisites: None 5 Scenes
Moved to main site
→
A-Gate Architecture
Now at /instrument/ — the full circuit, encoding, topology, and polarity mechanism.
→
Geometric Invariants
Now at /invariants/ — the hierarchy of measurable invariants with interactive scenes.
← Back to qdnu.ai Launch Visualization →