Basics of Complex Numbers
The imaginary unit and algebraic and geometric properties of complex numbers.
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Elementary Functional Analysis for Optimization
An introduction to the core concepts of functional analysis essential for understanding optimization theory in machine learning.
Elementary Functional Analysis: Why Types Matter in Optimization
Understanding the fundamental distinction between vectors and dual vectors—and why it's crucial for gradient-based optimization.
Motivating Hilbert Spaces: Encoding Geometry
Generalizing the dot product to function spaces and demanding completeness leads to Hilbert spaces, essential for geometry and analysis in infinite dimensions.
Motivating Banach Spaces: Norms Measure Size
Exploring why complete normed spaces without inner products (Banach spaces) are essential, with examples like Lp and C(K) spaces, and their impact on analysi...
RMS Norm
Characterizing properties of the Root-Mean-Square Norm for vectors
Matrix Norms: Foundations for Metrized Deep Learning
An introduction to matrix norms, their duals, and computational aspects essential for understanding advanced optimization in machine learning.
Properties of Matrix Norms
Characterizing some properties of matrix norms
Cheat Sheet: Elementary Functional Analysis for Optimization
A concise summary of core functional analysis concepts, emphasizing bra-ket notation, dual spaces, and transformation properties, crucial for machine learnin...