Algebra

2103 Submissions

[4] viXra:2103.0152 [pdf] submitted on 2021-03-24 20:20:16

Cramer's Rule for Overdetermined Systems of Linear Equations

Authors: Yanko Popov
Comments: 10 Pages.

In this article, with the help of introduced cross product in n-dimensional Euclidean space, the Jacobi identity and Cramer's rule for over-determined system of linear equations are displayed.
Category: Algebra

[3] viXra:2103.0085 [pdf] submitted on 2021-03-14 19:35:52

A Simple Criteria of Prime Numbers

Authors: Masami Yamane
Comments: 2 Pages. We present a simple criteria of prime numbers.

In this short note, we will propose a simple criteria for prime numbers and our mehtod seems to be that is practical. Our idea will have some connection with the famous Goldbach conjecture.
Category: Algebra

[2] viXra:2103.0071 [pdf] submitted on 2021-03-12 07:41:04

The D'alembert-Gauss Theorem

Authors: Antoine Balan
Comments: 2 pages, written in french

We give a geometric and topological proof of the d'Alembert-Gauss theorem: a complex polynomial has a root.
Category: Algebra

[1] viXra:2103.0029 [pdf] submitted on 2021-03-04 03:30:44

A Theorem on the Number of Distinct Eigenvalues

Authors: Rachid Marsli
Comments: 17 Pages.

A theorem on the number of distinct eigenvalues of diagonalizable matrices is obtained. Some applications related to matrices with simple eigenvalues, triangular defective matrices, adjacency matrices and graphs are discussed. Other ideas and examples are provided.
Category: Algebra