# orthogonality

Published articles for orthogonality.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## A Spectral Analysis of Moore Graphs

DevFeed: [A Spectral Analysis of Moore Graphs](<https://devfeed.tech/articles/a-spectral-analysis-of-moore-graphs-40406.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2016/11/03/a-spectral-analysis-of-moore-graphs/>)

Published: 2016-11-03T08:00:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [adjacency-matrix](<https://devfeed.tech/tags/adjacency-matrix.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [math](<https://devfeed.tech/tags/math.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [moore-graph](<https://devfeed.tech/tags/moore-graph.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [regular](<https://devfeed.tech/tags/regular.md>), [spectral-graph-theory](<https://devfeed.tech/tags/spectral-graph-theory.md>), [trace](<https://devfeed.tech/tags/trace.md>), [vertex](<https://devfeed.tech/tags/vertex.md>)

### AI overview

This mathematical article analyzes Moore graphs of girth 5 using the eigenvalues of their adjacency matrices. It derives the minimum vertex count and shows that the degree must be one of 3, 7, or 57.

### Source excerpt

For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$.

## The Fourier Series--A Primer

DevFeed: [The Fourier Series--A Primer](<https://devfeed.tech/articles/the-fourier-series-a-primer-40271.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/04/25/the-fourier-series/>)

Published: 2012-04-25T21:43:06Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [function](<https://devfeed.tech/topics/function.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [classification](<https://devfeed.tech/tags/classification.md>), [complex-analysis](<https://devfeed.tech/tags/complex-analysis.md>), [foundation](<https://devfeed.tech/tags/foundation.md>), [fourier-analysis](<https://devfeed.tech/tags/fourier-analysis.md>), [heat-equation](<https://devfeed.tech/tags/heat-equation.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [primer](<https://devfeed.tech/tags/primer.md>)

### AI overview

This primer introduces the mathematics of Fourier series, beginning with periodic functions and explaining how sine and cosine functions serve as building blocks for representing functions. It establishes foundational concepts for later work involving Fourier transforms, sound and image analysis, classification, and machine vision.

### Source excerpt

Overview In this primer we'll get a first taste of the mathematics that goes into the analysis of sound and images. In the next few primers, we'll be building the foundation for a number of projects in this domain: extracting features of music for classification, constructing so-called hybrid images, and other image manipulations for machine vision problems (for instance, for use in neural networks or support vector machines; we're planning on covering these topics in due time as well).

## Inner Product Spaces--A Primer

DevFeed: [Inner Product Spaces--A Primer](<https://devfeed.tech/articles/inner-product-spaces-a-primer-40231.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/07/25/inner-product-spaces-a-primer/>)

Published: 2011-07-25T00:29:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Computing](<https://devfeed.tech/topics/computing.md>)

Tags: [big-o-notation](<https://devfeed.tech/tags/big-o-notation.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [inner-product](<https://devfeed.tech/tags/inner-product.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>), [vector-spaces](<https://devfeed.tech/tags/vector-spaces.md>), [vectors](<https://devfeed.tech/tags/vectors.md>)

### AI overview

This primer explains why vector spaces can be extended with a dot-product-like operation and defines inner products through conjugate symmetry, linearity, additivity, and positive definiteness. It introduces inner product spaces and discusses their connection to linear functionals.

### Source excerpt

Vector spaces alone are not enough to do a lot of the interesting things we'd like them to do. Since a vector space is a generalization of Euclidean space, it is natural for us to investigate more specific types of vector spaces which are more akin to Euclidean space. In particular, we want to include the notion of a dot product. By admitting additional structure to a vector space, we may perform more computations, and hopefully get more interesting results.