# Algebra Commons™

## All Articles in Algebra

890 full-text articles. Page 5 of 33.

On A Frobenius Problem For Polynomials, 2017 Gettysburg College

#### On A Frobenius Problem For Polynomials, Ricardo Conceição, R. Gondim, M. Rodriguez

##### Math Faculty Publications

We extend the famous diophantine Frobenius problem to a ring of polynomials over a field~k. Similar to the classical problem we show that the n = 2 case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over ℤ to k[t] and give an algorithm to solve the Frobenius problem for polynomials over a field k of sufficiently large size.

The Common Invariant Subspace Problem And Tarski’S Theorem, 2017 Nicolaus Copernicus University of Toruń

#### The Common Invariant Subspace Problem And Tarski’S Theorem, Grzegorz Pastuszak

##### Electronic Journal of Linear Algebra

This article presents a computable criterion for the existence of a common invariant subspace of $n\times n$ complex matrices $A_{1}, \dots ,A_{s}$ of a fixed dimension $1\leq d\leq n$. The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski's theorem on quantifier elimination in the theory $\ACF$ of algebraically closed fields. This means that for an arbitrary formula $\varphi$ of the language of fields, a quantifier-free formula $\varphi'$ such that $\varphi\lra\varphi'$ in $\ACF$ is given explicitly. The construction of $\varphi'$ is ...

Refined Inertia Of Matrix Patterns, 2017 Redeemer University College

#### Refined Inertia Of Matrix Patterns, Kevin N. Vander Meulen, Jonathan Earl, Adam Van Tuyl

##### Electronic Journal of Linear Algebra

This paper explores how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. It demonstrates that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike what happens for nonzero patterns. A class of patterns is developed that are refined inertially arbitrary but not spectrally arbitrary, making use of the property of a properly signed nest. The paper includes a characterization of the inertially arbitrary and refined inertially arbitrary patterns of order three, as well as the patterns of order four with the least number of nonzero entries.

Decreasing Math Anxiety Through Teaching Quadratic Equations, 2017 The College at Brockport: State University of New York

#### Decreasing Math Anxiety Through Teaching Quadratic Equations, Kaitlyn Kaufman

##### Education and Human Development Master's Theses

Math anxiety is known as having a feeling of fear that interferes with math performance. Many students today suffer from math anxiety as they push through each developmental stage in their schooling. A majority of students develop math anxiety through traditional classroom methods, such as drill and practice, assessments, memorizing, and textbooks. According to research, teachers can help decrease math anxiety in students by incorporating specific teaching styles, methods, and strategies, related to decrease math anxiety, into lessons. These teaching styles, methods, and strategies include, but not limited to, constructivist teaching, concrete-to-representation-to-abstract model, student-centered learning, and interactive lessons. Based on ...

Properties Of K-Isotropic Functions, 2017 The University of Western Ontario