Identity Matrix
The square matrix with 1s on the diagonal and 0s elsewhere; the matrix no-op.
- Multiplicative identity for matrices.
- All eigenvalues are 1; orthogonal, diagonal, symmetric.
- Add αI to fix singular X^T X (ridge).
When to use: Initialization (residual streams ≈ identity), ridge regularization, sanity-check baselines.
Example: I_3 = [[1,0,0],[0,1,0],[0,0,1]]. Ridge: (X^T X + αI) θ = X^T y.