🏔️ Matrices, conquered. Here's the whole toolkit in one view.

What a matrix is:
• A grid of numbers that turns one vector into another: W x = y (each output = a row dotted with the input).
• Geometrically, it transforms space — and its columns show where the basis vectors land.
• Run it backwards with the inverse (W⁻¹y) to decode inputs from outputs — when possible.

Its personality:
• Determinant = area scaling (0 → collapses space, info lost).
• Rank = how many dimensions the outputs span; null space = what gets sent to zero.
• Eigenvectors = directions the matrix only scales; eigenvalues = by how much (complex → rotation).

Multiplying matrices chains transformations: C[i][j] = rowᵢ(A) · colⱼ(B), with inner dimensions matching.

🤖 Where it all goes: neural-net layers (matmul), PCA and embeddings (eigenvectors), model compression (rank), and network stability (eigenvalues). Next quest puts eigenvalues to work: predicting whether a circuit of neurons explodes, decays, or oscillates — just by reading two numbers. 🚀