Properties of Matrix Norms
Characterizing some properties of matrix norms
Collection-landing
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: A Crash Course for Optimization
An introduction to the core concepts of functional analysis, motivated by how different mathematical 'types' (kets and bras) behave under transformations, es...
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 L_p and C(K) spaces, and their impact on analys...
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.
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...