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A very short note on a problem of Godsil and Sun

Wei Wang

Abstract

Using the spectral theorem for symmetric matrices over a real closed field, we give a quick answer to a problem of Godsil and Sun on degree-similarity of graphs.

A very short note on a problem of Godsil and Sun

Abstract

Using the spectral theorem for symmetric matrices over a real closed field, we give a quick answer to a problem of Godsil and Sun on degree-similarity of graphs.

Paper Structure

This paper contains 1 section, 1 theorem, 2 equations.

Table of Contents

  1. Acknowledgments

Key Result

Theorem 1

Let $K$ and $L$ be two symmetric matrices over $\mathbb{Q}(\mu)$. Then the following two assertions are equivalent: (i)$\det(tI-K)=\det(tI-L)$; (ii)$K$ and $L$ are similar over $\mathbb{Q}(\mu)$.

Theorems & Definitions (1)

  • Theorem 1