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Articles 1  30 of 861
FullText Articles in Algebra
The Effects Of Motivation, Technology And Satisfaction On Student Achievement In FaceToFace And Online College Algebra Classes, Hanan Jamal Amro, MarieAnne Mundy, Lori Kupczynski
The Effects Of Motivation, Technology And Satisfaction On Student Achievement In FaceToFace And Online College Algebra Classes, Hanan Jamal Amro, MarieAnne Mundy, Lori Kupczynski
TxDLA Journal of Distance Learning
Demand for online learning has increased in recent years due to the convenience of class delivery. However, some students appear to have difficulties with online education resulting in lack of completion. The study utilized a quantitative approach with archival data and survey design. The factors of demographics, motivation, technology, and satisfaction were compared for facetoface and online students. MANCOVA tests were performed to analyze the data while controlling age and gender to uncover significant differences between the two groups. The sample and population for this study were predominantly Hispanic students.
Motivation and Technology were nonsignificant, but satisfaction was proven to ...
Application Of Jordan Algebra For Testing Hypotheses About Structure Of Mean Vector In Model With Block Compound Symmetric Covariance Structure, Roman Zmyślony, Ivan Zezula, Arkadiusz Kozioł
Application Of Jordan Algebra For Testing Hypotheses About Structure Of Mean Vector In Model With Block Compound Symmetric Covariance Structure, Roman Zmyślony, Ivan Zezula, Arkadiusz Kozioł
Electronic Journal of Linear Algebra
In this article authors derive test for structure of mean vector in model with block compound symmetric covariance structure for twolevel multivariate observations. One possible structure is so called structured mean vector when its components remain constant over sites or over time points, so that mean vector is of the form $\boldsymbol{1}_{u}\otimes\boldsymbol{\mu}$ with $\boldsymbol{\mu}=(\mu_1,\mu_2,\ldots,\mu_m)'\in\mathbb{R}^m$. This hypothesis is tested against alternative of unstructured mean vector, which can change over sites or over time points.
Inertia Sets Allowed By Matrix Patterns, Adam H. Berliner, Dale D. Olesky, Pauline Van Den Driessche
Inertia Sets Allowed By Matrix Patterns, Adam H. Berliner, Dale D. Olesky, Pauline Van Den Driessche
Electronic Journal of Linear Algebra
Motivated by the possible onset of instability in dynamical systems associated with a zero eigenvalue, sets of inertias $\sn_n$ and $\SN{n}$ for sign and zerononzero patterns, respectively, are introduced. For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n1,1)$, a sufficient condition is given for $\mc{A}$ and every superpattern of $\mc{A}$ to allow $\sn_n$, and a family of such irreducible sign patterns for all $n\geq 3$ is specified. All zerononzero patterns (up to equivalence) that allow $\SN{3}$ and $\SN{4}$ are determined, and are described by their associated digraphs.
Some Graphs Determined By Their Distance Spectrum, Stephen Drury, Huiqiu Lin
Some Graphs Determined By Their Distance Spectrum, Stephen Drury, Huiqiu Lin
Electronic Journal of Linear Algebra
Let $G$ be a connected graph with order $n$. Let $\lambda_1(D(G))\geq \cdots\geq \lambda_n(D(G))$ be the distance spectrum of $G$. In this paper, it is shown that the complements of $P_n$ and $C_n$ are determined by their $D$spectrum. Moreover, it is shown that the cycle $C_n$ ($n$ odd) is also determined by its $D$spectrum.
A Tensor's Torsion, Neil Steinburg
A Tensor's Torsion, Neil Steinburg
Dissertations, Theses, and Student Research Papers in Mathematics
While tensor products are quite prolific in commutative algebra, even some of their most basic properties remain relatively unknown. We explore one of these properties, namely a tensor's torsion. In particular, given any finitely generated modules, M and N over a ring R, the tensor product $M\otimes_R N$ almost always has nonzero torsion unless one of the modules M or N is free. Specifically, we look at which rings guarantee nonzero torsion in tensor products of nonfree modules over the ring. We conclude that a specific subclass of onedimensional Gorenstein rings will have this property.
Adviser: Roger Wiegand ...
On N/PAsymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices, Jolanta Maria Pielaszkiewicz, Dietrich Von Rosen, Martin Singull
On N/PAsymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices, Jolanta Maria Pielaszkiewicz, Dietrich Von Rosen, Martin Singull
Electronic Journal of Linear Algebra
The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.
A Note On The Matrix ArithmeticGeometric Mean Inequality, Teng Zhang
A Note On The Matrix ArithmeticGeometric Mean Inequality, Teng Zhang
Electronic Journal of Linear Algebra
This note proves the following inequality: If $n=3k$ for some positive integer $k$, then for any $n$ positive definite matrices $\bA_1,\bA_2,\dots,\bA_n$, the following inequality holds: \begin{equation*}\label{eq:main} \frac{1}{n^3} \, \Big\\sum_{j_1,j_2,j_3=1}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\ \,\geq\, \frac{(n3)!}{n!} \, \Big\\sum_{\substack{j_1,j_2,j_3=1,\\\text{$j_1$, $j_2$, $j_3$ all distinct}}}^{n}\bA_{j_1}\bA_{j_2}\bA_{j_3}\Big\, \end{equation*} where $\\cdot\$ represents the operator norm. This inequality is a special case of a recent conjecture proposed by Recht and R ...
Local Higher Category Theory, Nicholas Meadows
Local Higher Category Theory, Nicholas Meadows
Electronic Thesis and Dissertation Repository
The purpose of this thesis is to give presheaftheoretic versions of three of the main extant models of higher category theory: the Joyal, Rezk and Bergner model structures. The construction of these model structures takes up Chapters 2, 3 and 4 of the thesis, respectively. In each of the model structures, the weak equivalences are local or ‘stalkwise’ weak equivalences. In addition, it is shown that certain Quillen equivalences between the aforementioned models of higher category theory extend to Quillen equivalences between the various models of local higher category theory.
Throughout, a number of features of local higher category theory ...
Determining The Determinant, Danny Otero
Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, Maitreyee Chandramohan Kulkarni
Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, Maitreyee Chandramohan Kulkarni
LSU Doctoral Dissertations
This dissertation describes a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the wellstudied case of dimer models on a disc. We prove that all BerensteinFominZelevinsky quivers for Schubert cells in a symmetric KacMoody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.
Rank Function And Outer Inverses, Manjunatha Prasad Karantha, K. Nayan Bhat, Nupur Nandini Mishra
Rank Function And Outer Inverses, Manjunatha Prasad Karantha, K. Nayan Bhat, Nupur Nandini Mishra
Electronic Journal of Linear Algebra
For the class of matrices over a field, the notion of `rank of a matrix' as defined by `the dimension of subspace generated by columns of that matrix' is folklore and cannot be generalized to the class of matrices over an arbitrary commutative ring. The `determinantal rank' defined by the size of largest submatrix having nonzero determinant, which is same as the column rank of given matrix when the commutative ring under consideration is a field, was considered to be the best alternative for the `rank' in the class of matrices over a commutative ring. Even this determinantal rank and ...
Correlation Matrices With The Perron Frobenius Property, Phelim P. Boyle, Thierno B. N'Diaye
Correlation Matrices With The Perron Frobenius Property, Phelim P. Boyle, Thierno B. N'Diaye
Electronic Journal of Linear Algebra
This paper investigates conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the PerronFrobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are examined. The special structure of correlation matrices permits obtaining of detailed analytical results for low dimensional matrices. Some specific results for the $n$by$n$ case are also derived. This problem was motivated by an application in portfolio theory.
Simple Groups, Progenitors, And Related Topics, Angelica Baccari
Simple Groups, Progenitors, And Related Topics, Angelica Baccari
Electronic Theses, Projects, and Dissertations
The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w  pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive ...
Symmetric Presentations, Representations, And Related Topics, Adam Manriquez
Symmetric Presentations, Representations, And Related Topics, Adam Manriquez
Electronic Theses, Projects, and Dissertations
The purpose of this thesis is to develop original symmetric presentations of finite nonabelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J_{1}, the Mathieu group M_{12}, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2^{*60 }: (2 x A_{5}), 2^{*60 :} A_{5}, 2^{*56} : (2^{3 }: 7), and 2^{*28 }: (PGL(2,7):2), respectively. We have also discovered the groups ...
Galois Theory And The Quintic Equation, Yunye Jiang
Galois Theory And The Quintic Equation, Yunye Jiang
Honors Theses
Most students know the quadratic formula for the solution of the general quadratic polynomial in terms of its coefficients. There are also similar formulas for solutions of the general cubic and quartic polynomials. In these three cases, the roots can be expressed in terms of the coefficients using only basic algebra and radicals. We then say that the general quadratic, cubic, and quartic polynomials are solvable by radicals. The question then becomes: Is the general quintic polynomial solvable by radicals? Abel was the first to prove that it is not. In turn, Galois provided a general method of determining when ...
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 $2$.
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 ...
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 ...
Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon
Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon
Mathematics, Physics, and Computer Science Faculty Articles and Research
The class of nonassociative right hoops, or narhoops for short, is defined as a subclass of rightresiduated magmas, and is shown to be a variety. These algebras generalize both right quasigroups and right hoops, and we characterize the subvarieties in which the operation x ^^ y = (x/y)y is associative and/or commutative. Narhoops with a left unit are proved to be integral if and only if ^ is commutative, and their congruences are determined by the equivalence class of the left unit. We also prove that the four identities defining narhoops are independent.
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 ...
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 ...
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