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Articles 1  30 of 880
FullText Articles in Algebra
The Hermitian NullRange Of A Matrix Over A Finite Field, Edoardo Ballico
The Hermitian NullRange Of A Matrix Over A Finite Field, Edoardo Ballico
Electronic Journal of Linear Algebra
Let $q$ be a prime power. For $u=(u_1,\dots ,u_n), v=(v_1,\dots ,v_n)\in \mathbb {F} _{q^2}^n$, let $\langle u,v\rangle := \sum _{i=1}^{n} u_i^qv_i$ be the Hermitian form of $\mathbb {F} _{q^2}^n$. Fix an $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}$. In this paper, it is considered the case $k=0$ of the set $\mathrm{Num} _k(M):= \{\langle u,Mu\rangle \mid u\in \mathbb {F} _{q^2}^n, \langle u,u\rangle =k\}$. When $M$ has coefficients in $\mathbb {F ...
The Properties Of Partial Trace And Block Trace Operators Of Partitioned Matrices, Katarzyna Filipiak, Daniel Klein, Erika Vojtková
The Properties Of Partial Trace And Block Trace Operators Of Partitioned Matrices, Katarzyna Filipiak, Daniel Klein, Erika Vojtková
Electronic Journal of Linear Algebra
The aim of this paper is to give the properties of two linear operators defined on nonsquare partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positivedefiniteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multilevel multivariate models or in the theory of experiments for the determination of an optimal designs under ...
Preface: International Conference On Matrix Analysis And Its Applications  Mattriad 2017, Oskar Maria Baksalary, Natalia Bebiano, Heike Fassbender, Simo Puntanen
Preface: International Conference On Matrix Analysis And Its Applications  Mattriad 2017, Oskar Maria Baksalary, Natalia Bebiano, Heike Fassbender, Simo Puntanen
Electronic Journal of Linear Algebra
No abstract provided.
Norm Inequalities Related To Clarkson Inequalities, Fadi Alrimawi, Omar Hirzallah, Fuad Kittaneh
Norm Inequalities Related To Clarkson Inequalities, Fadi Alrimawi, Omar Hirzallah, Fuad Kittaneh
Electronic Journal of Linear Algebra
Let $A$ and $B$ be $n\times n$ matrices. It is shown that if $p=2$, $4\leq p<\infty$, or $2
Bounds For The Completely Positive Rank Of A Symmetric Matrix Over A Tropical Semiring, David Dolžan, Polona Oblak
Bounds For The Completely Positive Rank Of A Symmetric Matrix Over A Tropical Semiring, David Dolžan, Polona Oblak
Electronic Journal of Linear Algebra
In this paper, an upper bound for the CPrank of a matrix over a tropical semiring is obtained, according to the vertex clique cover of the graph prescribed by the positions of zero entries in the matrix. The graphs that beget the matrices with the lowest possible CPranks are studied, and it is proved that any such graph must have its diameter equal to $2$.
Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick
Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick
Research and Evaluation in Literacy and Technology
Reflecting upon my personal experiences teaching mathematics to English Language Learners (ELL) in a public high school in Lincoln, Nebraska, this essay largely focuses on the time I spent as the only Accelerated Math teacher in my school building. From 2012 – 2017, I taught three different subjects at this high school: Advanced Algebra, Algebra, and Accelerated Math. This essay highlights why I chose to become a math and ELL teacher, as well as the challenges, issues, struggles, and successes I experienced during my time teaching. I focus on the challenges I faced teaching students who did not share my native ...
Resolutions Of Finite Length Modules Over Complete Intersections, Seth Lindokken
Resolutions Of Finite Length Modules Over Complete Intersections, Seth Lindokken
Dissertations, Theses, and Student Research Papers in Mathematics
The structure of free resolutions of finite length modules over regular local rings has long been a topic of interest in commutative algebra. Conjectures by BuchsbaumEisenbudHorrocks and AvramovBuchweitz predict that in this setting the minimal free resolution of the residue field should give, in some sense, the smallest possible free resolution of a finite length module. Results of Tate and Shamash describing the minimal free resolution of the residue field over a local hypersurface ring, together with the theory of matrix factorizations developed by Eisenbud and EisenbudPeeva, suggest analogous lower bounds for the size of free resolutions of finite length ...
Tp Matrices And Tp Completability, Duo Wang
Tp Matrices And Tp Completability, Duo Wang
Undergraduate Honors Theses
A matrix is called totally nonnegative (TN) if the determinant of
every square submatrix is nonnegative and totally positive (TP)
if the determinant of every square submatrix is positive. The TP
(TN) completion problem asks which partial matrices have a TP
(TN) completion. In this paper, several new TPcompletable pat
terns in 3byn matrices are identied. The relationship between
expansion and completability is developed based on the prior re
sults about single unspecied entry. These results extend our un
derstanding of TPcompletable patterns. A new Ratio Theorem
related to TPcompletability is introduced in this paper, and it can
possibly be ...
Strongly Real Conjugacy Classes In Unitary Groups Over Fields Of Even Characteristic, Tanner N. Carawan
Strongly Real Conjugacy Classes In Unitary Groups Over Fields Of Even Characteristic, Tanner N. Carawan
Undergraduate Honors Theses
An element $g$ of a group $G$ is called strongly real if there is an $s$ in $G$ such that $s^2 = 1$ and $sgs^{1} = g^{1}$. It is a fact that if $g$ in $G$ is strongly real, then every element in its conjugacy class is strongly real. Thus we can classify each conjugacy class as strongly real or not strongly real. Gates, Singh, and Vinroot have classified the strongly real conjugacy classes of U$(n, q^2)$ in the case that $q$ is odd. Vinroot and Schaeffer Fry have classified some of the conjugacy classes of U ...
Counting Real Conjugacy Classes In Some Finite Classical Groups, Elena Amparo
Counting Real Conjugacy Classes In Some Finite Classical Groups, Elena Amparo
Undergraduate Honors Theses
An element $g$ in a group $G$ is real if there exists $x\in G$ such that $xgx^{1}=g^{1}$. If $g$ is real then all elements in the conjugacy class of $g$ are real. In \cite{GS1} and \cite{GS2}, Gill and Singh showed that the number of real $\mathrm{GL}_n(q)$conjugacy classes contained in $\mathrm{SL}_n(q)$ equals the number of real $\mathrm{PGL}_n(q)$conjugacy classes when $q$ is even or $n$ is odd. In this paper, we use generating functions to show that the result is also true for odd $q ...
Putting Fürer's Algorithm Into Practice With The Bpas Library, Linxiao Wang
Putting Fürer's Algorithm Into Practice With The Bpas Library, Linxiao Wang
Electronic Thesis and Dissertation Repository
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as other disciplines. In 1971, Schönhage and Strassen designed an algorithm that improved the multiplication time for two integers of at most n bits to O(log n log log n). In 2007, Martin Fürer presented a new algorithm that runs in O (n log n · 2 ^O(log* n)) , where log*n is the iterated logarithm of n. We explain how we can put Fürer’s ideas into practice for multiplying polynomials over a prime field Z/pZ, which characteristic is a Generalized ...
Upper Bound For The Number Of Distinct Eigenvalues Of A Perturbed Matrix, Sunyo Moon, Seungkook Park
Upper Bound For The Number Of Distinct Eigenvalues Of A Perturbed Matrix, Sunyo Moon, Seungkook Park
Electronic Journal of Linear Algebra
In 2016, Farrell presented an upper bound for the number of distinct eigenvalues of a perturbed matrix. Xu (2017), and Wang and Wu (2016) introduced upper bounds which are sharper than Farrell's bound. In this paper, the upper bounds given by Xu, and Wang and Wu are improved.
RangeCompatible Homomorphisms Over The Field With Two Elements, Clément De Seguins Pazzis
RangeCompatible Homomorphisms Over The Field With Two Elements, Clément De Seguins Pazzis
Electronic Journal of Linear Algebra
Let U and V be finitedimensional vector spaces over a field K, and S be a linear subspace of the space L(U, V ) of all linear operators from U to V. A map F : S → V is called rangecompatible when F(s) ∈ Im s for all s ∈ S. Previous work has classified all the rangecompatible group homomorphisms provided that codimL(U,V )S ≤ 2 dim V − 3, except in the special case when K has only two elements and codimL(U,V )S = 2 dim V − 3. This article gives a thorough treatment of that special case. The results ...
Linear Algebra (Ung), Hashim Saber, Beata Hebda, Piotr Hebda, Benkam Bobga
Linear Algebra (Ung), Hashim Saber, Beata Hebda, Piotr Hebda, Benkam Bobga
Mathematics Grants Collections
This Grants Collection for Linear Algebra was created under a Round Seven ALG Textbook Transformation Grant.
Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.
Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:
 Linked Syllabus
 Initial Proposal
 Final Report
Cayley Graphs Of Psl(2) Over Finite Commutative Rings, Kathleen Bell
Cayley Graphs Of Psl(2) Over Finite Commutative Rings, Kathleen Bell
Masters Theses & Specialist Projects
Hadwiger's conjecture is one of the deepest open questions in graph theory, and Cayley graphs are an applicable and useful subtopic of algebra.
Chapter 1 will introduce Hadwiger's conjecture and Cayley graphs, providing a summary of background information on those topics, and continuing by introducing our problem. Chapter 2 will provide necessary definitions. Chapter 3 will give a brief survey of background information and of the existing literature on Hadwiger's conjecture, Hamiltonicity, and the isoperimetric number; in this chapter we will explore what cases are already shown and what the most recent results are. Chapter 4 will ...
An Investigation Into The Properties Of Quaternions: Their Origin, Basic Properties, Functional Analysis, And Algebraic Characteristics, James Miller
Masters Essays
No abstract provided.
Potential Stability Of Matrix Sign Patterns, Christopher Hambric
Potential Stability Of Matrix Sign Patterns, Christopher Hambric
Undergraduate Honors Theses
The topic of matrix stability is very important for determining the stability of solutions to systems of differential equations. We examine several problems in the field of matrix stability, including minimal conditions for a $7\times7$ matrix sign pattern to be potentially stable, and applications of sign patterns to the study of Turing instability in the $3\times3$ case. Furthermore, some of our work serves as a model for a new method of approaching similar problems in the future.
Implementation And Analysis Of The Nonlinear Decomposition Attack On Polycyclic Groups, Yoongbok Lee
Implementation And Analysis Of The Nonlinear Decomposition Attack On Polycyclic Groups, Yoongbok Lee
Undergraduate Honors Theses
Around two years ago, Roman'kov introduced a new type of attack called the nonlinear decomposition attack on groups with solvable membership search problem. To analyze the precise efficiency of the algorithm, we implemented the algorithm on two protocols: semidirect product protocol and KoLee protocol. Because polycyclic groups were suggested as possible platform groups in the semidirect product protocol and polycyclic groups have a solvable membership search problem, we used poly cyclic groups as the platform group to test the attack. While the complexity could vary regarding many different factors within the group, there was always at least one exponential ...
Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton
Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Let S be a Riemann surface and G a large subgroup of Aut(S) (Aut(S) may be unknown). We are particularly interested in regular ngonal surfaces, i.e., the quotient surface S/G (and hence S/Aut(S)) has genus zero. For various H the ramification information of the branched coverings S/K > S/H may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of Aut(S). The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy ...
The Hafnian And A Commutative Analogue Of The Grassmann Algebra, Dmitry Efimov
The Hafnian And A Commutative Analogue Of The Grassmann Algebra, Dmitry Efimov
Electronic Journal of Linear Algebra
A close relationship between the determinant, the pfaffian, and the Grassmann algebra is wellknown. In this paper, a similar relation between the permanent, the hafnian, and a commutative analogue of the Grassmann algebra is described. Using the latter, some new properties of the hafnian are proved.
Extremal Copositive Matrices With Zero Supports Of Cardinality N2, Roland Hildebrand
Extremal Copositive Matrices With Zero Supports Of Cardinality N2, Roland Hildebrand
Electronic Journal of Linear Algebra
Let $A \in {\cal C}^n$ be an exceptional extremal copositive $n \times n$ matrix with positive diagonal. A zero $u$ of $A$ is a nonzero nonnegative vector such that $u^TAu = 0$. The support of a zero $u$ is the index set of the positive elements of $u$. A zero $u$ is minimal if there is no other zero $v$ such that $\Supp v \subset \Supp u$ strictly. Let $G$ be the graph on $n$ vertices which has an edge $(i,j)$ if and only if $A$ has a zero with support $\{1,\dots,n\} \setminus \{i,j\}$. In ...
Monomial Progenitors And Related Topics, Madai Obaid Alnominy
Monomial Progenitors And Related Topics, Madai Obaid Alnominy
Electronic Theses, Projects, and Dissertations
The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M_{11}, HS × D_{5}, where HS is the sporadic group HigmanSim group, the projective special unitary group U(3; 5) and the projective special linear group L_{2}(149) as homomorphic images of the monomial progenitors 11*^{4} :_{m} (5 :4), 5*^{6 } :_{m} S_{5} and 149*^{2 } :_{m } D_{37}. We have also discovered 2^{4} : S_{3} × C_{2}, 2 ...
Progenitors, Symmetric Presentations And Constructions, Diana Aguirre
Progenitors, Symmetric Presentations And Constructions, Diana Aguirre
Electronic Theses, Projects, and Dissertations
Abstract
In this project, we searched for new constructions and symmetric presentations of important groups, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. My target nonabelian simple groups included sporadic groups, linear groups, and alternating groups. In addition, we discovered finite groups as homomorphic images of progenitors and proved some of their isomorphism type and original symmetric presentations. In this thesis we found original symmeric presentations of M12, J1 and the simplectic groups S(4,4) and S(3,4) on various con trol groups. Using the technique of double coset enumeration we ...
Progenitors, Symmetric Presentations, And Related Topics, Joana Viridiana Luna
Progenitors, Symmetric Presentations, And Related Topics, Joana Viridiana Luna
Electronic Theses, Projects, and Dissertations
Abstract
A progenitor developed by Robert T. Curtis is a type of infinite groups formed by the semidirect product of a free group m∗n and a transitive permutation group of degree n. To produce finite homomorphic images we had to add relations to the progenitor of the form 2∗n : N. In this thesis we have investigated several permutations progenitors and monomials, 2∗12 : S4, 2∗12 : S4 × 2, 2∗13 : (13 : 4), 2∗30 : ((2• : 3) : 5), 2∗13 :13,2∗13 :(13:2),2∗13 :(13:S3),53∗2 :m (13:4),7∗8 :m (32 :8 ...
Algebraic Methods For The Construction Of AlgebraicDifference Equations With Desired Behavior, Lazaros Moysis, Nicholas Karampetakis
Algebraic Methods For The Construction Of AlgebraicDifference Equations With Desired Behavior, Lazaros Moysis, Nicholas Karampetakis
Electronic Journal of Linear Algebra
For a given system of algebraic and difference equations, written as an AutoRegressive (AR) representation $A(\sigma)\beta(k)=0$, where $\sigma $ denotes the shift forward operator and $A\left( \sigma \right) $ a regular polynomial matrix, the forwardbackward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of $A\left( \sigma \right) $. This work studies the inverse problem: Given a specific forwardbackward behavior, find a family of regular or nonregular polynomial matrices $A\left( \sigma \right) $, such that the constructed system $A\left( \sigma \right) \beta \left( k\right) =0$ has exactly the ...
Families Of Graphs With Maximum Nullity Equal To Zero Forcing Number, Joseph S. Alameda, Emelie Curl, Armando Grez, Leslie Hogben, O'Neill Kingston, Alex Schulte, Derek Young, Michael Young
Families Of Graphs With Maximum Nullity Equal To Zero Forcing Number, Joseph S. Alameda, Emelie Curl, Armando Grez, Leslie Hogben, O'Neill Kingston, Alex Schulte, Derek Young, Michael Young
Mathematics Publications
The maximum nullity of a simple graph G, denoted M(G), is the largest possible nullity over all symmetric real matrices whose ijth entry is nonzero exactly when fi, jg is an edge in G for i =6 j, and the iith entry is any real number. The zero forcing number of a simple graph G, denoted Z(G), is the minimum number of blue vertices needed to force all vertices of the graph blue by applying the color change rule. This research is motivated by the longstanding question of characterizing graphs G for which M(G) = Z(G). The ...
Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings  if they are studying the algorithms traditionally used by their ethic group  or simply to their sense of curiosity. Somewhat surprisingly, we show that one of these algorithms  a traditional Italian multiplication algorithm  is actually in some reasonable sense better than the algorithm that we all normally use  namely, it is easier to parallelize.
College Algebra Through Problem Solving (2018 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Dabkowska
College Algebra Through Problem Solving (2018 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Dabkowska
Open Educational Resources
This is a selfcontained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.
The Relationship Between KForcing And KPower Domination, Daniela Ferrero, Leslie Hogben, Franklin H.J. Kenter, Michael Young
The Relationship Between KForcing And KPower Domination, Daniela Ferrero, Leslie Hogben, Franklin H.J. Kenter, Michael Young
Mathematics Publications
Zero forcing and power domination are iterative processes on graphs where an initial set of vertices are observed, and additional vertices become observed based on some rules. In both cases, the goal is to eventually observe the entire graph using the fewest number of initial vertices. The concept of kpower domination was introduced by Chang et al. (2012) as a generalization of power domination and standard graph domination. Independently, kforcing was defined by Amos et al. (2015) to generalize zero forcing. In this paper, we combine the study of kforcing and kpower domination, providing a new approach to analyze both ...
Applications Of Analysis To The Determination Of The Minimum Number Of Distinct Eigenvalues Of A Graph, Beth Bjorkman, Leslie Hogben, Scarlitte Ponce, Carolyn Reinhart, Theodore Tranel
Applications Of Analysis To The Determination Of The Minimum Number Of Distinct Eigenvalues Of A Graph, Beth Bjorkman, Leslie Hogben, Scarlitte Ponce, Carolyn Reinhart, Theodore Tranel
Mathematics Publications
We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero offdiagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues of several families of graphs and small graphs.