This repository contains notes on the mathematical preliminaries for machine learning, originally conceived as supplementary notes to the Fall 2017 incarnation of Carnegie Mellon University's 10-715: Advanced Introduction to Machine Learning.
- Functions
- Metric Spaces
- Basic Definitions
- Limit and Continuity
- Complete Metric Spaces
- Compact Metric Spaces
- Normed Linear Spaces
- Vector Spaces
- Norm
- Euclidean Space
- Sequence Spaces
- Lebesgue Spaces
- Uniform Norm
- Operator Norm
- Matrix Operator Norm
- Frobenius Norm
- Norms on a Finite-Dimensional Normed Linear Space
- Inner Product Spaces
- Definitions and Examples
- Orthogonality
- Unitary Classification of Hilbert Spaces
- Hilbert Spaces with a Countable Orthonormal Basis
- Finite-Dimensional Hilbert Spaces
- Interlude: Basic Numerical Analysis
- NumPy
- Floating-Point Arithmetic
- Singular Value Decomposition
- Invertibility of Linear Operators and Matrices
- Singular Values
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Unless otherwise specified, the licensing details for this repository are as follows.
The notes are distributed with CC-by-4.0. The homework problems, taken from the 10-715 course page, are copyrighted by Barnabas Poczos. The written homework solutions are distributed with CC-by-4.0. Programming homework solutions are distributed with the MIT License.