Yongge Tian

发表

Ranks of Solutions of the Matrix Equation AXB = C

Yongge Tian, 2003 .

Some inequalities for sums of nonnegative definite matrices in quaternions

G. Styan, Yongge Tian, 2005 .

Rank equalities for idempotent matrices with applications

G. Styan, Yongge Tian, 2006 .

The maximal and minimal ranks of A − BXC with applications

Yongge Tian, Shizhen Cheng, 2003 .

Ranks of Hermitian and skew-Hermitian solutions to the matrix equation AXA∗=B

Yoshio Takane, Yongge Tian, Y. Takane, 2009 .

Equalities and inequalities for inertias of hermitian matrices with applications

Yongge Tian, Yongge Tian, 2010 .

Maximization and minimization of the rank and inertia of the Hermitian matrix expression A — BX — (BX)* with applications

Yongge Tian, 2011 .

Solving the matrix inequality AXB + (AXB)^* ⩾ C

D. Rosen, Yongge Tian, 2012 .

Analytical solutions to some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix inequalities

Yongge Tian, 2013, 1301.0986.

Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method

Yongge Tian, 2012 .

The solvability of two linear matrix equations

Yongge Tian, 2000 .

RANK AND INERTIA OF SUBMATRICES OF THE MOORE-PENROSE INVERSE OF A HERMITIAN MATRIX ∗

Yongge Tian, Yongge Tian, 2010 .

Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors

Yongge Tian, 2011 .

Formulas for calculating the extremal ranks and inertias of a matrix-valued function subject to matrix equation restrictions

Yongge Tian, 2013, 1301.2850.

Extremal ranks of submatrices in an Hermitian solution to the matrix equation AXA*=B with applications

Yongge Tian, Yonghui Liu, 2010 .

COMPLETING BLOCK HERMITIAN MATRICES WITH MAXIMAL AND MINIMAL RANKS AND INERTIAS

Yongge Tian, Yongge Tian, 2010 .

On Additive Decomposition of the Hermitian Solution of the Matrix Equation AXA* = B

Yongge Tian, 2012 .

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

Yongge Tian, 2002 .

PARTIALLY SUPERFLUOUS OBSERVATIONS

Yongge Tian, Hailong Qian, Yongge Tian, 2006, Econometric Theory.

On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model

Douglas P. Wiens, Yongge Tian, D. Wiens, 2006 .

Rank equalities related to generalized inverses of matrices and their applications

Yongge Tian, Yongge Tian, 1999 .

The Minimum Rank of a 3 × 3 Partial Block Matrix

Yongge Tian, Yongge Tian, 2002 .

How to use RSVD to solve the matrix equation A=BXC

Yongge Tian, Yonghui Liu, 2010 .

Optimization problems on the rank and inertia of the Hermitian matrix expression A − BX − ( BX ) ∗ with applications

Yongge Tian, 2010 .

Rank and inertia optimizations of two Hermitian quadratic matrix functions subject to restrictions with applications

Yongge Tian, Ying Li, 2010 .

Rank equalities for idempotent and involutary matrices

Yongge Tian, George P. H. Styan, G. Styan, 2001 .

Rank equalities related to outer inverses of matrices and applications

Yongge Tian, Yongge Tian, 2001 .

Rank Equalities for Block Matrices and Their Moore-Penrose Inverses

Yongge Tian, Yongge Tian, 2004 .

Matrix rank/inertia formulas for least-squares solutions with statistical applications

Yongge Tian, Bo Jiang, 2016 .

Matrix representations of octonions and their applications

Yongge Tian, 2000, math/0003166.

Completing triangular block matrices with maximal and minimal ranks

Yongge Tian, 2000 .

Matrix Theory over the Complex Quaternion Algebra

Yongge Tian, Yongge Tian, 2000 .

Some properties of projectors associated with the WLSE under a general linear model

Yoshio Takane, Yongge Tian, Y. Takane, 2008 .

LinearModels and Regression Analysis On SumDecompositions ofWeighted Least-Squares Estimators for the Partitioned LinearModel

Y. Takane, Yongge Tian, 2007 .

On relationships between two linear subspaces and two orthogonal projectors

Yongge Tian, 2019, Special Matrices.

Matrix rank and inertia formulas in the analysis of general linear models

Yongge Tian, 2017 .

Decomposition of approaches of a general linear model with fixed parameters

Yongge Tian, Bo Jiang, 2017 .

A matrix handling of predictions of new observations under a general random-effects model

Yongge Tian, 2015 .

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

Yongge Tian, Bo Jiang, 2016 .

Equivalence of predictors under real and over-parameterized linear models

Yongge Tian, Shengjun Gan, Yongge Tian, 2017 .

Two competing linear random-effects models and their connections

Yongge Tian, Chang-Yu Lu, Yuqin Sun, 2018 .

More on generalized inverses of partitioned matrices with Banachiewicz–Schur forms

Yoshio Takane, Yongge Tian, Y. Takane, 2009 .

The Maximal and Minimal Ranks of a Quadratic Matrix Expression with Applications

Yongge Tian, 2002 .

Some algebraic and statistical properties of WLSEs under a general growth curve model

Y. Takane, Yongge Tian, 2007 .

Some overall properties of seemingly unrelated regression models

Yongge Tian, Yuqin Sun, Rongzhe Ke, 2014 .

D-optimal Designs for a Combined Simple Linear and Haar-Wavelet Regression Model

A. Herzberg, Yongge Tian, 2006 .

Efficiency of Optimal Designs for a Linear Haar-Wavelet Regression

Yongge Tian, 2010 .

A comparison between two competing fixed parameter constrained general linear models with new regressors

Yongge Tian, Chang-Yu Lu, Yuqin Sun, 2018 .

On decompositions of estimators under a general linear model with partial parameter restrictions

Yongge Tian, Bo Jiang, Xuan Zhang, 2017 .

Some remarks on general linear model with new regressors

Yongge Tian, Chang-Yu Lu, Shengjun Gan, 2015 .

On properties of BLUEs under general linear regression models

Yongge Tian, 2013 .

Miscellaneous reverse order laws for generalized inverses of matrix products with applications

Yongge Tian, 2020 .

Two groups of mixed reverse order laws for generalized inverses of two and three matrix products

Yongge Tian, 2020, Comput. Appl. Math..

A family of 512 reverse order laws for generalized inverses of a matrix product: A review

Yongge Tian, 2020, Heliyon.

Linear Statistical Models, Least-Squares Estimators, and Classication Analysis to Reverse-Order Laws for Generalized Inverses of Matrix Products

Yongge Tian, 2018 .

Biquaternions and their complex matrix representations

Yongge Tian, 2013 .

Max-min optimizations on the rank and inertia of a linear Hermitian matrix expression subject to range , rank and definiteness restrictions

Yongge Tian, 2010 .

Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications

Yongge Tian, 2012 .

A general prediction analysis to linear random-effects models with restrictions and new observations

Yongge Tian, 2015 .

Miscellaneous reverse order laws for generalized inverses of matrix products with applications

Yongge Tian, 2020, Advances in Operator Theory.

Analytical formulas for calculating ranks, dimensions, orthogonal projectors, and ranges of matrices composed of Kronecker products

Yongge Tian, 2020 .

Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions

Yongge Tian, 2014 .

On global optimizations of the rank and inertia of the matrix function A 1 − B 1 XB ∗ 1 subject to a pair of matrix equations

Yongge Tian, 2011 .

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

Yongge Tian, 2017 .

Closed-form formulas for calculating the extremal ranks and inertias of a quadratic matrix-valued function and their applications

Yongge Tian, 2013, 1301.2567.

Analytical formulas for calculating extremal ranks and inertias of quadratic matrix-valued functions and their applications

Yongge Tian, 2012 .

A new algebraic analysis to linear mixed models

Yongge Tian, 2016 .

Some Mixed-Type Reverse-Order Laws for the Moore-Penrose Inverse of a Triple Matrix Product

Yongge Tian, 2007 .

Some identities for Moore–Penrose inverses of matrix products

Yongge Tian, Shizhen Cheng †, 2004 .

Rank equalities related to generalized inverses of matrices and their applications

Yongge Tian, 2000, math/0003224.

Yongge Tian, 1998, math-ph/0003032.

Extremal quadratic properties of least-squares solutions of a linear matrix equation with statistical applications

Yongge Tian, Bo Jiang, 2016 .

Some remarks on fundamental formulas and facts in the statistical analysis of a constrained general linear model

Yongge Tian, Jie Wang, 2018, Communications in Statistics - Theory and Methods.

Matrix Theory over the Complex Quaternion Algebra

Yongge Tian, 2000, math/0004005.

Necessary and sufficient conditions for nonlinear matrix identities to always hold

Yongge Tian, Bo Jiang, 2018, Aequationes mathematicae.

Some notes on linear sufficiency

S. Puntanen, Yongge Tian, R. Kala, 2015, Statistical Papers.

On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models

Yongge Tian, Chang-Yu Lu, Yuqin Sun, 2012, Metrika.

A study of range equalities for mixed products of two matrices and their generalized inverses

Yongge Tian, 2022, Computational and Applied Mathematics.

Expansion Formulas for Orthogonal Projectors onto Ranges of Row Block Matrices

Yongge Tian, Yufu Wang, 2014 .

Rank/inertia approaches to weighted least-squares solutions of linear matrix equations

Bo Jiang, Yongge Tian, Yongge Tian, 2017, Appl. Math. Comput..

Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Bo Jiang, Yongge Tian, Yongge Tian, 2017, Comput. Stat..

On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model

Yongge Tian, Xuan Zhang, 2016 .

Cochran's statistical theorem revisited

Yongge Tian, George P.H. Styan, G. Styan, 2006 .

A-minimax and D-minimax robust optimal designs for approximately linear Haar-wavelet models

Agnes M. Herzberg, Yongge Tian, A. Herzberg, 2006, Comput. Stat. Data Anal..

Estimation and optimal designs for linear Haar-wavelet models

Agnes M. Herzberg, Yongge Tian, A. Herzberg, 2007 .

The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems

Yoshio Takane, Yongge Tian, Y. Takane, 2009, Comput. Math. Appl..

On additive decompositions of estimators under a multivariate general linear model and its two submodels

Bo Jiang, Yongge Tian, Yongge Tian, 2017, J. Multivar. Anal..

On decompositions of BLUEs under a partitioned linear model with restrictions

Yongge Tian, Xuan Zhang, 2016 .

On decompositions of BLUEs under a partitioned linear model with restrictions

Yongge Tian, Xuan Zhang, 2014, Statistical Papers.

On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models

Yongge Tian, Chang-Yu Lu, Yuqin Sun, 2013 .

On an additive decomposition of the BLUE in a multiple-partitioned linear model

Yongge Tian, Yongge Tian, 2009, J. Multivar. Anal..

On Sum Decompositions of Weighted Least-Squares Estimators for the Partitioned Linear Model

Y. Takane, Yongge Tian, 2007 .

Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model

Yongge Tian, 2007 .

The equalities of ordinary least-squares estimators and best linear unbiased estimators for the restricted linear model

D. Wiens, Yongge Tian, 2006 .

On equivalence of predictors/estimators under a multivariate general linear model with augmentation

Yongge Tian, Bo Jiang, 2017 .

Equalities for estimators of partial parameters under linear model with restrictions

Bo Jiang, Yongge Tian, Yongge Tian, 2016, J. Multivar. Anal..

Some overall properties of seemingly unrelated regression models

Yongge Tian, Yuqin Sun, Rong Ke, 2013, AStA Advances in Statistical Analysis.

Some equalities for estimations of partial coefficients under a general linear regression model

Yongge Tian, Jieping Zhang, 2011 .

A simultaneous decomposition of a matrix triplet with applications

Yongge Tian, Yonghui Liu, Yongge Tian, 2011, Numer. Linear Algebra Appl..

On additive decompositions of solutions of the matrix equation AXB=C

Yongge Tian, 2010 .

Estimations of parametric functions under a system of linear regression equations with correlated errors

Yongge Tian, 2010 .

On additive and block decompositions of WLSEs under a multiple partitioned regression model

Yongge Tian, Zhe Tian, 2010 .

On equalities for BLUEs under misspecified Gauss-Markov models

Yongge Tian, Yong Ge Tian, 2009 .

On the equivalence of estimations under a general linear model and its transformed models

Yongge Tian, Simo Puntanen, S. Puntanen, 2009 .

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

Yongge Tian, Yongge Tian, 2009, Appl. Math. Comput..

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

Yongge Tian, George P.H. Styan, G. Styan, 2005 .

THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL

G. Styan, S. Puntanen, Yongge Tian, 2005, Econometric Theory.

More on maximal and minimal ranks of Schur complements with applications

Yongge Tian, Yongge Tian, 2004, Appl. Math. Comput..

The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices

Yongge Tian, Yongge Tian, 2002 .

Statistical inference of a partitioned linear random-effects model

Yongge Tian, Ming Liu, Ruixia Yuan, 2021, Communications in Statistics - Theory and Methods.

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

Yongge Tian, Rong Ma, 2020, Linear and Multilinear Algebra.

On comparison of dispersion matrices of estimators under a constrained linear model

Yongge Tian, Wenxing Guo, Yongge Tian, 2016, Stat. Methods Appl..

A new derivation of BLUPs under random-effects model

Yongge Tian, 2015 .

On relations between BLUEs under two transformed linear models

Yongge Tian, Wenxing Guo, Baomin Dong, 2014, J. Multivar. Anal..

On the natural restrictions in the singular Gauss–Markov model

Yongge Tian, M. Beisiegel, E. Dagenais, 2008 .

Transformation approaches of linear random-effects models

Yongge Tian, 2017, Statistical Methods & Applications.

Transformation approaches of linear random-effects models

Yongge Tian, Yongge Tian, 2017, Stat. Methods Appl..

Some notes on linear sufficiency

Yongge Tian, Simo Puntanen, Radosław Kala, 2017 .

Characterizing Relationships Between Estimations Under a General Linear Model with Explicit and Implicit Restrictions by Rank of Matrix

Yongge Tian, 2012 .

On equalities of estimations of parametric functions under a general linear model and its restricted models

Yongge Tian, 2010 .

Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model

Yongge Tian, 2010 .

Some equalities for estimations of variance components in a general linear model and its restricted and transformed models

Chunmei Liu, Yongge Tian, Yongge Tian, 2010, J. Multivar. Anal..

Some equalities and inequalities for covariance matrices of estimators under linear model

Yongge Tian, 2017 .

On comparison of dispersion matrices of estimators under a constrained linear model

Yongge Tian, Wenxing Guo, 2016, Statistical Methods & Applications.

More on extremal ranks of the matrix expressions A − BX ± X*B* with statistical applications

Yongge Tian, Yonghui Liu, Yongge Tian, 2008, Numer. Linear Algebra Appl..

Statistical analysis of a linear regression model with restrictions and superfluous variables

Yongge Tian, Wenming Li, Ruixia Yuan, 2022, Journal of Industrial and Management Optimization.

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

Yoshio Takane, Yongge Tian, Y. Takane, 2009 .

On simultaneous prediction in a multivariate general linear model with future observations

Yongge Tian, Cheng Wang, 2017 .

A new analysis of the relationships between a general linear model and its mis-specified forms

Yongge Tian, Bo Jiang, 2017 .

A MATRIX HANDLING OF PREDICTIONS UNDER A GENERAL LINEAR RANDOM-EFFECTS MODEL WITH NEW OBSERVATIONS

Yongge Tian, 2015 .

Solving Two Pairs of Quadratic Equations in Quaternions

Yongge Tian, 2010 .

Universal Factorization Equalities for Quaternion Matrices and Their Applications

Yongge Tian, 1999 .

HOW TO ESTABLISH UNIVERSAL BLOCK-MATRIX FACTORIZATIONS ∗

Yongge Tian, George P. H. Styan, G. Styan, 2001 .

Yongge Tian, 1999, math-ph/0003031.

Biquaternions and their complex matrix representations

Yongge Tian, 2012, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry.

Reverse order laws for the generalized inverses of multiple matrix products

Yongge Tian, Yongge Tian, 1994 .

Schur complements and Banachiewicz-Schur forms

Yoshio Takane, Yongge Tian, Y. Takane, 2005 .

Simultaneous optimal predictions under two seemingly unrelated linear random-effects models

Yongge Tian, Pengyang Xie, 2020, Journal of Industrial & Management Optimization.

Analysis of transformations of linear random-effects models

Yongge Tian, 2016 .

Twists of two or multiple idempotent matrices

Yongge Tian, 2019, 1911.03715.

Computation and comparison of estimators under different linear random-effects models

Yongge Tian, Changli Lu, Shengjun Gan, 2020, Commun. Stat. Simul. Comput..

Yongge Tian, Bo Jiang, Ming-Te Liu, 2022, Mathematica Slovaca.

Yongge Tian, 2000, math/0003167.

Yongge Tian, 2005 .

A new derivation of BLUPs under random-effects model

Yongge Tian, 2015, Metrika.

A survey on rank and inertia optimization problems of the matrix-valued function $A + BXB^{*}$

Yongge Tian, 2015 .

Some rank equalities and inequalities for Kronecker products of matrices

Yongge Tian, Yongge Tian, 2005 .

Rank equalities and inequalities for Kronecker products of matrices with applications

Yongge Tian, Jianjun Chuai, Yongge Tian, 2004, Appl. Math. Comput..

Max-Min Problems on the Ranks and Inertias of the Matrix Expressions A−BXC±(BXC)∗ with Applications

Yongge Tian, Yonghui Liu, Yongge Tian, 2011, J. Optim. Theory Appl..

Matrix representations of octonions and their applications

Yongge Tian, 2000, math/0003166.

How to solve three fundamental linear matrix inequalities in the Löwner partial ordering pdf

Yongge Tian, Yongge Tian, 2013, ArXiv.

Characterization of Relationships Between the Domains of Two Linear Matrix-Valued Functions with Applications

Yongge Tian, 2020 .

Formulas for calculating the dimensions of the sums and the intersections of a family of linear subspaces with applications

Yongge Tian, 2019, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry.

Formulas for calculating the dimensions of the sums and the intersections of a family of linear subspaces with applications

Yongge Tian, 2019, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry.

Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products

Yongge Tian, 2022, Axioms.

Equivalence analysis of different reverse order laws for generalized inverses of a matrix product

Yongge Tian, 2021, Indian Journal of Pure and Applied Mathematics.

Reverse order laws for generalized inverses of products of two or three matrices with applications

Yongge Tian, 2019, 1912.05948.

Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications

Yongge Tian, 2016 .

On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product

Yoshio Takane, Yongge Tian, Y. Takane, 2007 .

The equivalence between ( AB )†= B † A † and other mixed-type reverse-order laws

Yongge Tian, 2006 .

Generalized Inverses of Multiple Matrix Products

Yongge Tian, 2002 .

Miscellaneous reverse order laws and their equivalent facts for generalized inverses of a triple matrix product

Yongge Tian, 2021, AIMS Mathematics.

Matrix equalities equivalent to the reverse order law ( AB ) † = B † A †

Yongge Tian, 2020 .

A revisit to a reverse-order law for generalized inverses of a matrix product and its variations

Yongge Tian, 2017 .

Formulas for calculating the maximum and minimum ranks of products of generalized inverses of matrices

Yongge Tian, 2015 .

On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product

Yongge Tian, Yongge Tian, 2004, Int. J. Math. Math. Sci..

Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products

Yongge Tian, Yongge Tian, 2004, Appl. Math. Comput..

The Equations ax − xb = c , ax − x̄b = c and x̄ax = b in Quaternions

Yongge Tian, 2017 .

Analytical formulas for calculating the extremal ranks of the matrix-valued function $A + BXC$ when the rank of $X$ is fixed

Yongge Tian, 2013, 1301.3675.

Extremal Ranks of Some Symmetric Matrix Expressions with Applications

Yongge Tian, Yonghui Liu, Yongge Tian, 2006, SIAM J. Matrix Anal. Appl..

Twosetsofnewcharacterizationsfornormaland EP matrices

Yongge Tian, Yongge Tian, Shizhen Cheng, 2003 .

SPECIAL FORMS OF GENERALIZED INVERSES OF ROW BLOCK MATRICES

Yongge Tian, 2005 .

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

Yongge Tian, George P. H. Styan, G. Styan, 2002 .

RANKS AND INDEPENDENCE OF SOLUTIONS OF THE MATRIX EQUATION AXB + CY D = M

Yongge Tian, 2006 .

Solving Some Linear Equations Over Alternative Rings

Yongge Tian, 2010 .

Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models

Yongge Tian, Bo Jiang, 2022, Mathematics.

A prediction analysis in a constrained multivariate general linear model with future observations

Yongge Tian, Yuqin Sun, Hong Jiang, 2019, Communications in Statistics - Theory and Methods.

Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Yongge Tian, Bo Jiang, 2016, Computational Statistics.

Two competing linear random-effects models and their connections

Yongge Tian, Chang-Yu Lu, Yuqin Sun, 2016, Statistical Papers.

A study of the equivalence of inference results in the contexts of true and misspecified multivariate general linear models

Yongge Tian, Bo Jiang, Ruixia Yuan, 2023, AIMS Mathematics.

On best linear unbiased estimation and prediction under a constrained linear random-effects model

Yongge Tian, Bo Jiang, 2021, Journal of Industrial & Management Optimization.

Solutions of a constrained Hermitian matrix-valued function optimization problem with applications

Yongge Tian, 2016 .

A pr 2 00 0 MATRIX REPRESENTATIONS OF OCTONIONS AND THEIR APPLICATIONS

Yongge Tian, 2000 .