SciGit

Each note is one Markdown file. Notes state theorems, definitions, assumptions and observations. When a note uses, cites or mentions a statement of another note, both notes show the link.

16 notes · 33 links

Most linked notes

1. Inner product

   Real inner products, the norm of an inner product, and the Cauchy–Schwarz inequality.

2. Orthogonal projection

   Projection onto a finite-dimensional subspace, its characterization, and the Pythagorean theorem.

3. Hilbert spaces

   Complete inner product spaces, projection onto a closed convex set, and the Riesz theorem.

4. Expectation

   The expectation of an integrable random variable and its basic properties.

5. Convexity

   Convex functions, the finite Jensen inequality, and the first-order condition.

6. Variance

   Variance, the König–Huygens formula, and the Chebyshev inequality.

7. Gradient descent

   Gradient descent converges at rate O(1/k) on a smooth convex function.

8. Jensen inequality

   The probabilistic form of the convexity inequality.

9. Falsifiability

   Popper's demarcation criterion and the problem of auxiliary assumptions.

10. Least squares

    The least-squares estimator is an orthogonal projection.