# Algebra

## 1912 Submissions

 viXra:1912.0529 [pdf] submitted on 2019-12-31 05:39:24

### On a Local Spectra Inequality

Authors: Theophilus Agama

In this note we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log |t-\lambda_i|\}_{[||a||,||b||]}&\leq \# \mathrm{Spec}(ab^T)\log\bigg(\frac{||b||+||a||}{2}\bigg)\nonumber \\&+\frac{1}{||b||-||a||}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^T)}\log \bigg(1-\frac{2\lambda_i}{||b||+||a||}\bigg).\nonumber \end{align}Also under the same condition, the inequality also holds\begin{align}\int \limits_{||a||}^{||b||}\log|\mathrm{det}(ab^{T}-tI)|dt&\leq \# \mathrm{Spec}(ab^T)(||b||-||a||)\log\bigg(\frac{||b||+||a||}{2}\bigg)\nonumber \\&+\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^T)}\log \bigg(1-\frac{2\lambda_i}{||b||+||a||}\bigg).\nonumber \end{align}
Category: Algebra

 viXra:1912.0435 [pdf] submitted on 2019-12-24 03:27:19

### On Linear Algebra

Authors: Henry Wong

Category: Algebra

 viXra:1912.0073 [pdf] submitted on 2019-12-04 07:10:56

### V={e, (1 2)(3 4), (1 3)(2 4),(1 4)(2 3)} is a Characteristic Subgroup of the Alternating Group of Degree 4

Authors: Henry Wong