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1

Problems and Solutions

Andrew Cusamano, Kenneth Fogarty, Angelo S. DiDomenico, Yongge Tian, Ovidui Furdui, José Luis Díaz-Barrero, Ovidiu Furdui, Northwestern University Math Problem Solving Group, David Callan, Rob Pratt,

Journal:

College Mathematics Journal

Year:

2005

Language:

english

File:

PDF, 816 KB

english, 2005

2

Matrix representations of octonions and their applications

Journal:

Advances in Applied Clifford Algebras

Year:

2000

Language:

english

File:

PDF, 982 KB

english, 2000

3

Solving Two Pairs of Quadratic Equations in Quaternions

Journal:

Advances in Applied Clifford Algebras

Year:

2010

Language:

english

File:

PDF, 151 KB

english, 2010

4

Problems

Albert F. S. Wong, David Callan, Achilleas Sinefakopoulos, Zhang Yun, Yongge Tian, Elias Lampakis, Murray S. Klamkin, Árpád Bényi, Mircea Martin, Cornelius Stallmann, Gerald Thompson, Jean Bogaert, Co

Journal:

Mathematics Magazine

Year:

2004

Language:

english

File:

PDF, 605 KB

english, 2004

5

Problems and Solutions

Nora Thornber, William P. Wardlaw, Yongge Tian, Mohammad Riazi-Kermani, Hongbiao Zeng, José Luis Díaz-Barrero, Monte J. Zerger, Michael Andreoli, Michael Scott McClendon, Raymond N. Greenwell, Will Go

Journal:

College Mathematics Journal

Year:

2005

Language:

english

File:

PDF, 666 KB

english, 2005

6

Rank equalities for idempotent and involutary matrices

Yongge Tian, George P.H. Styan

Journal:

Linear Algebra and its Applications

Year:

2001

Language:

english

File:

PDF, 115 KB

english, 2001

7

Biquaternions and their complex matrix representations

Journal:

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Year:

2013

Language:

english

File:

PDF, 253 KB

english, 2013

8

Reverse order laws for the generalized inverses of multiple matrix products

Journal:

Linear Algebra and its Applications

Year:

1994

Language:

english

File:

PDF, 783 KB

english, 1994

9

Distributions of eigenvalues and inertias of some block Hermitian matrices consisting of orthogonal projectors

Tian, Yongge, Li, Ying

Journal:

Linear and Multilinear Algebra

Year:

2012

Language:

english

File:

PDF, 278 KB

english, 2012

10

10776

Journal:

American Mathematical Monthly

Year:

2000

Language:

english

File:

PDF, 134 KB

english, 2000

11

Inequalities Involving Rank and Kronecker Product: 11129

Yongge Tian and Robin Chapman

Journal:

American Mathematical Monthly

Year:

2006

Language:

english

File:

PDF, 158 KB

english, 2006

12

How to Express a Parallel Sum of k Matrices

Journal:

Journal of Mathematical Analysis and Applications

Year:

2002

Language:

english

File:

PDF, 79 KB

english, 2002

13

Cochran's statistical theorem revisited

Yongge Tian, George P.H. Styan

Journal:

Journal of Statistical Planning and Inference

Year:

2006

Language:

english

File:

PDF, 125 KB

english, 2006

14

Universal similarity factorization equalities over real Clifford algebras

Journal:

Advances in Applied Clifford Algebras

Year:

1998

Language:

english

File:

PDF, 1.25 MB

english, 1998

15

Equalities for orthogonal projectors and their operations

Journal:

Central European Journal of Mathematics

Year:

2010

Language:

english

File:

PDF, 333 KB

english, 2010

16

Matrix Systems with the Same Sets: 11146

Yongge Tian and Eugene A. Herman

Journal:

American Mathematical Monthly

Year:

2007

Language:

english

File:

PDF, 203 KB

english, 2007

17

Predicting noise-induced critical transitions in bistable systems

Ma, Jinzhong, Xu, Yong, Li, Yongge, Tian, Ruilan, Kurths, Jürgen

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2019

Language:

english

File:

PDF, 1.53 MB

english, 2019

18

Upper and lower bounds for ranks of matrix expressions using generalized inverses

Journal:

Linear Algebra and its Applications

Year:

2002

Language:

english

File:

PDF, 171 KB

english, 2002

19

Rank equalities and inequalities for Kronecker products of matrices with applications

Jianjun Chuai, Yongge Tian

Journal:

Applied Mathematics and Computation

Year:

2004

Language:

english

File:

PDF, 199 KB

english, 2004

20

Similarity and consimilarity of elements in the real Cayley-Dickson algebras

Journal:

Advances in Applied Clifford Algebras

Year:

1999

Language:

english

File:

PDF, 507 KB

english, 1999

21

On V-orthogonal projectors associated with a semi-norm

Yongge Tian, Yoshio Takane

Journal:

Annals of the Institute of Statistical Mathematics

Year:

2009

Language:

english

File:

PDF, 204 KB

english, 2009

22

On consistency, natural restrictions and estimability under classical and extended growth curve models

Yongge Tian, Yoshio Takane

Journal:

Journal of Statistical Planning and Inference

Year:

2009

Language:

english

File:

PDF, 231 KB

english, 2009

23

Hermitian-type generalized singular value decomposition with applications

Yonghui Liu, Yongge Tian

Journal:

Numerical Linear Algebra with Applications

Year:

2012

Language:

english

File:

PDF, 120 KB

english, 2012

24

Some rank equalities and inequalities for Kronecker products of matrices

Journal:

Linear and Multilinear Algebra

Year:

2005

Language:

english

File:

PDF, 129 KB

english, 2005

25

Some overall properties of seemingly unrelated regression models

Sun, Yuqin, Ke, Rong, Tian, Yongge

Journal:

AStA Advances in Statistical Analysis

Year:

2014

Language:

english

File:

PDF, 228 KB

english, 2014

26

Two universal similarity factorization equalities for commutative involutory and idempotent matrices and their applications

Journal:

Linear and Multilinear Algebra

Year:

2011

Language:

english

File:

PDF, 174 KB

english, 2011

27

The Moore–Penrose inverse for sums of matrices under rank additivity conditions

Journal:

Linear and Multilinear Algebra

Year:

2005

Language:

english

File:

PDF, 199 KB

english, 2005

28

On the Inverse of a Product of Orthogonal Projectors: 11112

Journal:

American Mathematical Monthly

Year:

2006

Language:

english

File:

PDF, 277 KB

english, 2006

29

11112

Journal:

American Mathematical Monthly

Year:

2004

Language:

english

File:

PDF, 147 KB

english, 2004

30

When does rank(ABC) = rank(AB) + rank(BC) - rank(B) hold?

Tian, Yongge, Styan, George P. H.

Journal:

International Journal of Mathematical Education

Year:

2002

Language:

english

File:

PDF, 205 KB

english, 2002

31

11040

Journal:

American Mathematical Monthly

Year:

2003

Language:

english

File:

PDF, 161 KB

english, 2003

32

10984

Journal:

American Mathematical Monthly

Year:

2003

Language:

english

File:

PDF, 130 KB

english, 2003

33

Squashing a Matrix by Adding an Imaginary Part: 10776

Yongge Tian and David W. Carter

Journal:

American Mathematical Monthly

Year:

2002

Language:

english

File:

PDF, 103 KB

english, 2002

34

Range Identities for Hermitian Idempotent Matrices: 11040

Yongge Tian and BSI Problems Group

Journal:

American Mathematical Monthly

Year:

2005

Language:

english

File:

PDF, 166 KB

english, 2005

35

11146

Journal:

American Mathematical Monthly

Year:

2005

Language:

english

File:

PDF, 176 KB

english, 2005

36

11466

Journal:

American Mathematical Monthly

Year:

2009

Language:

english

File:

PDF, 185 KB

english, 2009

37

11129

Journal:

American Mathematical Monthly

Year:

2005

Language:

english

File:

PDF, 179 KB

english, 2005

38

Polybrominated diphenyl ethers (PBDEs) and alternative brominated flame retardants (aBFRs) in sediments from four bays of the Yellow Sea, North China

Zhen, Xiaomei, Tang, Jianhui, Xie, Zhiyong, Wang, Runmei, Huang, Guopei, Zheng, Qian, Zhang, Kai, Sun, Yongge, Tian, Chongguo, Pan, Xiaohui, Li, Jun, Zhang, Gan

Journal:

Environmental Pollution

Year:

2016

Language:

english

File:

PDF, 1.18 MB

english, 2016

39

An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices

Tian, Yongge, Jiang, Bo

Journal:

Linear and Multilinear Algebra

Year:

2016

Language:

english

File:

PDF, 416 KB

english, 2016

40

Injective Properties of Complex Matrices: 10984

Yongge Tian and Carl Meyer

Journal:

American Mathematical Monthly

Year:

2004

Language:

english

File:

PDF, 153 KB

english, 2004

41

Upper and lower bounds for the rank of the matrix-valued function when X has a fixed rank

Journal:

Linear and Multilinear Algebra

Year:

2017

Language:

english

File:

PDF, 1.32 MB

english, 2017

42

The reverse-order law $(AB)^{\dag}=B^{\dag}(A^{\dag}ABB^{\dag})^{\dag}A^{\dag}$ and its equivalent equalities

Journal:

Journal of Mathematics of Kyoto University

Year:

2005

Language:

english

File:

PDF, 128 KB

english, 2005

43

Closed-form formulas for calculating the max–min ranks of a triple matrix product composed by generalized inverses

Tian, Yongge, Jiang, Bo

Journal:

Computational & Applied Mathematics

Year:

2018

Language:

english

File:

PDF, 807 KB

english, 2018

44

Fabrication and rheological behavior of tape‐casting slurry for ultra‐thin multilayer transparent ceramics

Zhao, Han, Tang, Fei, Xie, Yongzhen, Wen, Zicheng, Tian, Kangzhen, Nie, Xinming, Cao, Yongge, Tang, Dingyuan

Journal:

International Journal of Applied Ceramic Technology

Year:

2019

Language:

english

File:

PDF, 27.02 MB

english, 2019

45

Fabrication and rheological behavior of tape‐casting slurry for ultra‐thin multilayer transparent ceramics

Zhao, Han, Tang, Fei, Xie, Yongzhen, Wen, Zicheng, Tian, Kangzhen, Nie, Xinming, Cao, Yongge, Tang, Dingyuan

Journal:

International Journal of Applied Ceramic Technology

Year:

2019

File:

PDF, 27.02 MB

2019

46

Universal Decomposition Equalities for Operator Matrices in a Hilbert Space

Jiang, Bo, Tian, Yongge

Journal:

Complex Analysis and Operator Theory

Year:

2020

File:

PDF, 298 KB

2020

47

A matrix approach to a general partitioned linear model with partial parameter restrictions

Ma, Rong, Tian, Yongge

Journal:

Linear and Multilinear Algebra

Year:

2020

File:

PDF, 1.54 MB

2020

48

More on extremal ranks of the matrix expressions A − BX ± XB with statistical applications

Yonghui Liu, Yongge Tian

Journal:

Numerical Linear Algebra with Applications

Year:

2008

Language:

english

File:

PDF, 141 KB

english, 2008

49

A simultaneous decomposition of a matrix triplet with applications

Yonghui Liu, Yongge Tian

Journal:

Numerical Linear Algebra with Applications

Year:

2011

Language:

english

File:

PDF, 129 KB

english, 2011

50

Approximation and continuity of Moore–Penrose inverses of orthogonal row block matrices

Journal:

Applied Mathematics and Computation

Year:

2009

Language:

english

File:

PDF, 186 KB

english, 2009

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