SelectedWorks - Lei Cao

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Selected Works of Lei Cao

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About Lei Cao

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August 2019 - Present	Assistant Professor, Nova Southeastern University ‐ Halmos College of Arts and Sciences - Department of Mathematics
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2015 - 2019	Assistant Professor, Georgian Court University
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2013 - 2015	Visiting Assistant Professor (Post-Doctoral), Drexel University
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2012 - 2013	Visiting Assistant Professor, Bethel College - North Newton
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2007 - 2012	Teaching Assistant, Drexel University
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Disciplines

Physical Sciences and Mathematics

Research Interests

Combinatorial matrix theory, linear and multilinear algebra, and Graph Theory

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Courses

MA 2200 Statistics
MA 1250 Trigonometry
MA 2100 Calculus I

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June 2012	Ph.D. Mathematics, Drexel University
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ORCID

http://orcid.org/0000-0001-7613-7191

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Articles
Presentations

Articles (21)

Tridiagonal and Pentadiagonal Doubly Stochastic Matrices (Lei Cao, Darian McLaren and Sarah Plosker) arXiv (2020)

We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which ...

Pattern-Avoiding (0,1)-Matrices (Richard Brualdi and Lei Cao) arXiv (2020)

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We ...

Symmetric and Hankel-Symmetric Transportation Polytopes (Lei Cao, Zhi Chen, Qiang Li, et al.) Linear and Multilinear Algebra (2020)

In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&h;(R,S), which is the convex set of all symmetric and Hankel-symmetric non-negative matrices with prescribed row sum vector R and prescribed column sum vector ...

A Short Note on Extreme Points of Certain Polytopes (Lei Cao, Ariana Hall and Selcuk Koyuncu) Special Matrices (2020)

We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly substochastic matrices. In addition, we ...

Inequalities for Permanents and Permanental Minors of Row Substochastic Matrices (Zhi Chen, Jiawei Li, Lizhen Yang, et al.) Electronic Journal of Linear Algebra (2019)

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix ...

Centrosymmetric Stochastic Matrices (Lei Cao, Darian McLaren and Sarah Plosker) arXiv.org (2019)

We consider the convex set Γm,n of m×n stochastic matrices and the convex set Γπm,n ⊂Γm,n of m×n centrosymmetric stochastic matrices (stochastic matrices that are symmetric under rotation by 180 degrees). For Γm,n, we demonstrate ...

A Note on Multilevel Toeplitz Matrices (Lei Cao and Selcuk Koyuncu) Special Matrices (2019)

Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the ...

A Minimal Completion of (0, 1)-Matrices Without Total Support (Lei Cao) Linear and Multilinear Algebra (2019)

In this paper, we provide a method to complete a (0, 1)-matrix without total support via the minimal doubly stochastic completion of doubly substochastic matrices and show that the size of the completion is determined ...

Partitions of the Polytope of Doubly Substochastic Matrices (Lei Cao and Zhi Chen) Linear Algebra and its Applications (2019)

In this paper, we provide three different ways to partition the polytope of doubly substochastic matrices into subpolytopes via the prescribed row and column sums, the sum of all elements and the sub-defect respectively. Then ...

Diagonal Sums of Doubly Substochastic Matrices (Lei Cao, Zhi Chen, Xuefeng Duan, et al.) Electronic Journal of Linear Algebra (2019)

Let Ωn denote the convex polytope of all n x n doubly stochastic matrices, and ωn denote the convex polytope of all n x n doubly substochastic matrices. For a matrix A ϵ ωn, define ...

The Extreme Points of Certain Polytopes of Doubly Substochastic Matrices (Zhi Chen, Lei Cao and Qing-Wen Wang) Centrosymmetric matrices, Dobuly substochastic matrices, Extreme points (2019)

Let ωπn and ωt&h;n denote the convex polytope of n×n centrosymmetric doubly substochastic matrices and the convex polytope of n×n symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize ...

The Minimum Completions and Covers of Symmetric, Hankel Symmetric, and Centrosymmetric Doubly Substochastic Matrices (Jinze Song, Huili Liu, Hao Rong, et al.) Missouri Journal of Mathematical Sciences (2019)

In this paper, we investigate and describe all the minimal completions and covers of the symmetric, Hankel symmetric, and centrosymmetric doubly substochastic matrices, respectively.

On the Maximum of the Permanent of (I − A) (Zhi Chen and Lei Cao) Linear Algebra and its Applications (2018)

Let ω8n and ~ω8n denote the convex sets of doubly substochastic matrices and row substochastic matrices with the sum of all entries equal to s, respectively. In this paper, we give the upper bound of ...

Real Zero Polynomials and A. Horn's Problem (Lei Cao and Hugo J. Woerdeman) Linear Algebra and its Applications (2018)

A. Horn's problem concerns finding two self adjoint matrices, so that A, B, and A + B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable ...

Permanents of Doubly Substochastic Matrices (Lei Cao, Zhi Chen, Selcuk Koyuncu, et al.) Linear and Multilinear Algebra (2018)

Let ωn,k denote the convex polytope of doubly substochastic matrices with sub-defect k. Let h(A) and l(A) denote the maximum and minimum diagonals of A ϵ ωn,k respectively. In this paper, we study the relation ...

Partitions of Equiangular Tight Frames (James Rosado, Hieu D. Nguyen and Lei Cao) Linear Algebra and its Applications (2017)

We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which ...

Sub-Defect of Product of Doubly Substochastic Matrices (Lei Cao and Selcuk Koyuncu) Linear and Multilinear Algebra (2017)

The sub-defect of an n x n doubly substochastic matrix S, denoted by sd(S), is defined to be the smallest integer k such that there exists an (n + k) x (n + k) doubly ...

A Minimal Completion of Doubly Substochastic Matrix (Lei Cao, Selcuk Koyuncu and Timmothy Parmer) Linear and Multilinear Algebra (2016)

Let B be an n x n doubly substochastic matrix and let s be the sum of all entries of B. In this paper, we show that B has a sub-defect of k, which can ...

Symmetric Integer Matrices Having Integer Eigenvalues (Lei Cao and Selcuk Koyuncu) International Journal of Mathematics and Mathematical Sciences (2016)

We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and ...

On the Construction of Jacobi Matrices from Mixed data (Lei Cao and Yilin Yang) Alabama Journal of Mathematics (2015)

We show that a unique Jacobi matrix can be reconstructed from two types of mixed data: 1. its two eigenpairs, 2. its eigenvalues and the eigenvalues of its submatrix obtained by removing the first two ...

A Normal Variation of the Horn Problem: The Rank 1 Case (Lei Cao and Hugo J. Woerdeman) Annals of Functional Analysis (2014)

Given three n-tuples {λi}ni=1, {μi}ni=1, {vi}ni=1 of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that σ(A) = {λi}ni=1, σ(B) = {μi}ni=1, and σ(A+B) ...

Presentations (11)

Hankel Tournament and Special Oriented Graphs (Lei Cao and Richard Brualdi) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2019)

A Hankel tournament T of order n (an n X n Hankel tournament matrix T = [tij]) is a tournament such that i → j and edge implies (n + 1 - j) → (n ...

Sub-defect of Product of Doubly Substochastic Matrices (Selcuk Koyuncu and Lei Cao) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2019)

The sub-defect of an n x n doubly substochastic matrix S, denoted by sd(S); is defined to be the smallest integer k such that there exists an (n + k) x (n + k) doubly ...

The Extreme Points of Certain Polytopes (Richard Brualdi and Lei Cao) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2019)

We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these poly- topes and classify their extreme points. We also ...

Partitions on the Polytope of Doubly Substochastic Matrices (Lei Cao) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2018)

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