George P. H. Styan

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All published works

Action	Title	Year	Authors
+	The Legend of the Equality of OLSE and BLUE: Highlighted by C. R. Rao in 1967	2021	Augustyn Markiewicz Simo Puntanen George P. H. Styan
+ PDF Chat	Ingram Olkin (1924–2016): An Appreciation for a People Person	2019	Simo Puntanen George P. H. Styan
+	Around a Formula for the Rank of a Matrix Product with Some Statistical Applications	2017	Jerzy K. Baksalary George P. H. Styan
+	RANK CONDITIONS FOR GENERALIZED INVERSES OF PARTITIONED MATRICES	2016	George Marsaglia George P. H. Styan
+	Samuelson–Nair Inequality	2014	Henry Wolkowicz George P. H. Styan
+	Generalized Inverses	2014	George P. H. Styan
+	Random Vectors and Linear Statistical Models	2013	Simo Puntanen George P. H. Styan
+	Multivariate Statistical Analysis	2013	Simo Puntanen George A. F. Seber George P. H. Styan
+	Block-Diagonalization and the Schur Complement	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	Best Linear Unbiased Estimation in Linear Models	2011	Simo Puntanen George P. H. Styan
+	Nonnegative Definiteness of a Partitioned Matrix	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	Disjointness of Column Spaces	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	The Cauchy–Schwarz Inequality	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	Minimizing cov(y - Fx)	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	The Matrix $$\dot{\rm M}$$	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	A Decomposition of the Orthogonal Projector	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	Easy Column Space Tricks	2011	Simo Puntanen George P. H. Styan Jarkko Isotalo
+	Comments on 4×4 Philatelic Latin Squares	2010	P. D. Loly George P. H. Styan
+	On a matrix decomposition of Hartwig and Spindelböck	2009	Oskar Maria Baksalary George P. H. Styan Götz Trenkler
+	Some Comments on the Watson Efficiency of the Ordinary Least Squares Estimator Under the Gauss Markov Model	2009	Simo Puntanen George P. H. Styan
+	On some matrix equalities for generalized inverses with applications	2009	Yongge Tian George P. H. Styan
+	Stochastic Stamps: A Philatelic Introduction to Chance	2008	Simo Puntanen George P. H. Styan
+	The BLUE's covariance matrix revisited: A review	2008	Jarkko Isotalo Simo Puntanen George P. H. Styan
+	The Bulletin of the International Linear Algebra Society	2008	Hans‐Joachim Werner Steven J. Leon Roger C. Thompson George P. H. Styan Hans‐Joachim Werner Bryan L. Shader Oskar Maria Baksalary James Weaver
+	Decomposing matrices with Jerzy K. Baksalary	2008	Simo Puntanen George P. H. Styan
+	HUA'S MATRIX EQUALITY AND SCHUR COMPLEMENTS	2008	Christopher C. Paige George P. H. Styan Bo Ying Wang Fuzhen Zhang
+ PDF Chat	A Philatelic Excursion with Jeff Hunter in Probability and Matrix Theory	2007	George P. H. Styan Götz Trenkler
+	Random Vectors and Linear Statistical Models	2006	Simo Puntanen George P. H. Styan
+	Matrix Tricks for Linear Statistical Models: A Short Review of our Personal Top Fourteen	2006	Jarkko Isotalo Simo Puntanen George P. H. Styan
+	The General Expressions for the Moments of the Stochastic Shrinkage Parameters of the Liu Type Estimator	2006	Fikri Akdeniz George P. H. Styan Hans‐Joachim Werner
+	Generalized Inverses	2005	George P. H. Styan
+	Samuelson-Nair Inequality	2005	Henry Wolkowicz George P. H. Styan
+	Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms	2005	Yongge Tian George P. H. Styan
+	Rank equalities for idempotent matrices with applications	2005	Yongge Tian George P. H. Styan
+	THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL	2005	Simo Puntanen George P. H. Styan Yongge Tian
+	Some further results concerning the decomposition of the Watson efficiency in partitioned linear models	2005	Ka Lok Chu Jarkko Isotalo Simo Puntanen George P. H. Styan
+	Some comments on the life and work of Jerzy K. Baksalary (1944-2005)	2005	Oskar Maria Baksalary George P. H. Styan
+	Cochran's statistical theorem revisited	2004	Yongge Tian George P. H. Styan
+	<scp>S</scp> amuelson– <scp>N</scp> air Inequality	2004	Henry Wolkowicz George P. H. Styan
+	On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model	2004	Ka Lok Chu Jarkko Isotalo Simo Puntanen George P. H. Styan
+	02.4.2. On the Rank of a Matrix Useful in Goodness-of-Fit Testing of Structural Equation Models —Solution	2003	Simo Puntanen George P. H. Styan Hans‐Joachim Werner
+	02.1.2. A Particular Symmetric Idempotent Matrix—Solution	2003	George P. H. Styan Hans‐Joachim Werner
+	On a fundamental upper limit for the open-circuit resistance measurable between any two terminals of a positive resistance network	2002	S.W. Drury George P. H. Styan G.E. Subak-Sharpe
+	A necessary condition for the realization of a resistive n-port based on network size and on the concept of weighted terminal valency	2002	G.E. Subak-Sharpe George P. H. Styan
+	Generalized inverses of partitioned matrices in Banachiewicz–Schur form	2002	Jerzy K. Baksalary George P. H. Styan
+	Idempotency of linear combinations of an idempotent matrix and a tripotent matrix	2002	Jerzy K. Baksalary Oskar Maria Baksalary George P. H. Styan
+	When does rank(ABC) = rank(AB) + rank(BC) - rank(B) hold?	2002	Yongge Tian George P. H. Styan
+	Some comments on several matrix inequalities with applications to canonical correlations: Historical background and recent developments	2002	S.W. Drury Shuangzhe Liu Chang-Yu Lu Simo Puntanen George P. H. Styan
+	When does rank(<I>ABC</I>) = rank(<I>AB</I>) + rank(<I>BC</I>) - rank(<I>B</I>) hold?	2002	Yongge Tian George P. H. Styan
+	Rank equalities for idempotent and involutary matrices	2001	Yongge Tian George P. H. Styan
+ PDF Chat	How to establish universal block-matrix factorizations	2001	Yongge Tian George P. H. Styan
+	Two matrix-based proofs that the linear estimator Gy is the best linear unbiased estimator	2000	Simo Puntanen George P. H. Styan Hans‐Joachim Werner
+	Some Comments and a Bibliography on the Frucht—Kantorovich and Wielandt Inequalities	2000	Gülhan Alpargu George P. H. Styan
+	Some Comments and a Bibliography on the Laguerre-Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory	1999	Shane T. Jensen George P. H. Styan
+	Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor	1997	Geoffrey S. Watson Gülhan Alpargu George P. H. Styan
+	Inequalities and equalities associated with the campbell-youla generalized inverse of the indefinite admittance matrix of resistive networks	1997	George P. H. Styan G.E. Subak-Sharpe
+	Some remarks and a bibliography on the Kantorovich inequality	1996	Gülhan Alpargu George P. H. Styan
+	The Moore-Penrose Generalized Inverse of a Symmetric Matrix	1996	Simo Puntanen George P. H. Styan
+	On some characterizations of pairwise star orthogonality using rank and dagger additivity and subtractivity	1996	Robert E. Hartwig Matjaž Omladič Peter Šemrl George P. H. Styan
+	Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications	1996	‎Josip Pečarić Simo Puntanen George P. H. Styan
+	A note on rank additivity and range additivity	1996	Jerzy K. Baksalary Peter Šemrl George P. H. Styan
+	A brief biography and appreciation of Calyampudi Radhakrishna Rao, with a bibliography of his books and papers	1996	Simo Puntanen George P. H. Styan
+	SHORTED MATRICES AND THEIR APPLICATIONS IN LINEAR STATISTICAL MODELS: A REVIEW	1995	Sujit Kumar Mitra Simo Puntanen George P. H. Styan
+	The Singular Value Decomposition of the Square Roots of the Identity Matrix	1995	Jacob K. Goeree Heinz Neudecker S.W. Drury George P. H. Styan
+ PDF Chat	On some distributional properties of quadratic forms in normal variables and on some associated matrix partial orderings	1994	Jerzy K. Baksalary Jan Hauke George P. H. Styan
+	Linear algebra and statistics: Second special issue	1990	Michael D. Perlman Friedrich Pukelsheim George P. H. Styan
+	Löwner-ordering antitonicity of generalized inverse of Hermitian matrices	1990	Jerzy K. Baksalary Kenneth Nordström George P. H. Styan
+	The collected papers of T.W. Anderson, 1943-1985	1990	T. W. Anderson George P. H. Styan
+	The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator	1989	Simo Puntanen George P. H. Styan
+	[The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator]: Reply	1989	Simo Puntanen George P. H. Styan
+	The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator	1989	Simo Puntanen George P. H. Styan
+	Some properties of matrix partial orderings	1989	Jerzy K. Baksalary Friedrich Pukelsheim George P. H. Styan
+	THREE USEFUL EXPRESSIONS FOR EXPECTATIONS INVOLVING A WISHART MATRIX AND ITS INVERSE	1989	George P. H. Styan
+	Applied matrix algebra in the statistical sciences. By Alexander Basilevsky. Elsevier Science Publishing Co. (North‐Holland), Inc., New York, 1983. xiii + 389 pp. ISBN 0–444–00756–3	1987	George P. H. Styan
+	Topics in applied statistics. Edited by Yogendra P. Chaubey and Tryambakeshwar D. Dwivedi. Proceedings of Statistics '81 Canada Conference held at Concordia University, Montreal, Canada, April 29‐May 1, 1981. Dept. of Mathematics, Concordia University, Montreal, Quebec. ii + 808 + [7] pp. 1984, C. $120.00	1987	George P. H. Styan
+	On some characterizations of the “star” partial ordering for matrices and rank subtractivity	1986	Robert E. Hartwig George P. H. Styan
+	On a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys	1985	Alastair J. Scott George P. H. Styan
+	Matrix correlation	1984	J. O. Ramsay Jos ten Berge George P. H. Styan
+	RANK ADDITIVITY AND MATRIX POLYNOMIALS	1983	George P. H. Styan Akimichi Takemura
+	A Review and Some Extensions of Takemura's Generalizations of Cochrans's Theorem	1982	George P. H. Styan
+	Rank Additivity and Matrix Polynomials.	1982	George P. H. Styan Akimichi Takemura
+ PDF Chat	Some Inequalities Involving Statistical Expressions (L. V. Foster)	1982	Jonathan M. Borwein George P. H. Styan Henry Wolkowicz
+ PDF Chat	On the Existence and Uniqueness of the Maximum Likelihood Estimate of a Vector-Valued Parameter in Fixed-Size Samples	1981	Timo Mäkeläinen Klaus D. Schmidt George P. H. Styan
+	On Lavoie's determinantal inequality	1981	George P. H. Styan
+	More bounds for elgenvalues using traces	1980	Henry Wolkowicz George P. H. Styan
+	Bounds for eigenvalues using traces	1980	Henry Wolkowicz George P. H. Styan
+	Extensions of Samuelson's Inequality	1979	Henry Wolkowicz George P. H. Styan
+	Extensions of Samuelson's Inequality	1979	Henry Wolkowicz George P. H. Styan
+	Estimability and testability in restricted linear models<sup>1</sup>	1979	I. S. Alalouf George P. H. Styan
+	International encyclopedia of statistics William H. Kruskal Judith M. Tanur. The free press, New York, and Collier Macmillan, London and Toronto, 1978. Volume 1, A‐N, and volume 2, O‐Z and index, xxi + 1350 pp. $100.00. ISBN 0‐02‐917960‐2. [16 pp. Prospectus available free from the publishers.]	1979	George P. H. Styan
+	Uncorrelated residuals from linear models	1978	Warren T. Dent George P. H. Styan
+ PDF Chat	Nonnegative Definiteness of the Estimated Dispersion Matrix in a Multivariate Linear Model	1978	Friedrich Pukelsheim George P. H. Styan
+	Serial correlation and distributions on the shere	1976	D. A. S. Fraser Irwin Guttman George P. H. Styan
+	Book reviews	1976	Larry J. Gerstein H. Mochizuki George P. H. Styan D. Ž Djoković Alston Householder Alan J. Hoffman C.J. Maxson
+	Computation of the stationary distribution of a markov chain	1975	Christopher C. Paige George P. H. Styan P. Wächter
+	Equalities and Inequalities for Ranks of Matrices<sup>†</sup>	1974	George Matsaglia George P. H. Styan
+	The convergence of Markov chains with nonstationary transition probabilities and constant causative matrix	1973	Norman J. Pullman George P. H. Styan
+	Numerical computations for univariate linear models	1973	Gene H. Golub George P. H. Styan
+	Hadamard products and multivariate statistical analysis	1973	George P. H. Styan
+	A BIBLIOGRAPHY OF DISCRIMINANT ANALYSIS	1973	T. Cacoullos George P. H. Styan
+	Optimality Properties of Theil's BLUS Residuals	1972	Stanley I. Grossman George P. H. Styan
+ PDF Chat	When Does Rank(<i>A</i>+<i>B</i>)=Rank(<i>A</i>)+Rank(<i>B</i>)?	1972	George Marsaglia George P. H. Styan
+	Optimality Properties of Theil's BLUS Residuals	1972	Stanley I. Grossman George P. H. Styan
+ PDF Chat	A Matrix Approach to Nonstationary Chains	1970	Frank Harary Benjamin Lipstein George P. H. Styan
+ PDF Chat	Notes on the Distribution of Quadratic Forms in Singular Normal Variables	1970	George P. H. Styan
+ PDF Chat	Notes on the distribution of quadratic forms in singular normal variables	1970	George P. H. Styan
+	Inference in Multivariate Normal Populations with Structure. Part 2: Inference When Correlations Have Structure	1969	George P. H. Styan
+	Inference in Multivariate Normal Populations with Structure. Part 1: Inference on Variances When Correlations Are Known	1968	George P. H. Styan

Common Coauthors

Coauthor	Papers Together
Simo Puntanen	32
Jarkko Isotalo	12
Yongge Tian	9
Henry Wolkowicz	8
Jerzy K. Baksalary	7
Hans‐Joachim Werner	5
Oskar Maria Baksalary	4
Gülhan Alpargu	3
G.E. Subak-Sharpe	3
Friedrich Pukelsheim	3
S.W. Drury	3
Stanley I. Grossman	2
Christopher C. Paige	2
Götz Trenkler	2
Ka Lok Chu	2
George Marsaglia	2
Robert E. Hartwig	2
Akimichi Takemura	2
Peter Šemrl	2
C.J. Maxson	1
H. Mochizuki	1
Norman J. Pullman	1
George Matsaglia	1
Benjamin Lipstein	1
Irwin Guttman	1
Chang-Yu Lu	1
George A. F. Seber	1
P. D. Loly	1
Jan Hauke	1
P. Wächter	1
Jacob K. Goeree	1
Kenneth Nordström	1
Heinz Neudecker	1
T. Cacoullos	1
Matjaž Omladič	1
Jonathan M. Borwein	1
Fuzhen Zhang	1
Alastair J. Scott	1
Roger C. Thompson	1
Gene H. Golub	1
Geoffrey S. Watson	1
J. O. Ramsay	1
Frank Harary	1
T. W. Anderson	1
Alan J. Hoffman	1
Michael D. Perlman	1
D. A. S. Fraser	1
Bryan L. Shader	1
Augustyn Markiewicz	1
James Weaver	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Equalities and Inequalities for Ranks of Matrices<sup>†</sup>	1974	George Matsaglia George P. H. Styan	25
+	Generalized Inverse of Matrices and its Applications	1972	Alan J. Mayne	15
+	Generalized Inverse of Matrices and Its Applications	1973	K. S. Banerjee	15
+ PDF Chat	Inequalities: Theory of Majorization and its Applications.	1981	Barry C. Arnold Albert W. Marshall Ingram Olkin	9
+	The inefficiency of least squares	1975	Peter Bloomfield Geoffrey S. Watson	8
+	Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix	1973	C. Radhakrishna Rao	8
+ PDF Chat	Inequalities of Chebyshev Type Involving Conditional Expectations	1969	C. L. Mallows Donald H. Richter	7
+	The inefficiency of least squares: extensions of the kantorovich inequality	1985	C. Radhakrishna Rao	7
+	On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure	1969	George Zyskind Frank B. Martin	7
+	Schur complements and statistics	1981	Diane Valérie Ouellette	7
+ PDF Chat	On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models	1967	George Zyskind	7
+	Bounds for eigenvalues using traces	1980	Henry Wolkowicz George P. H. Styan	7
+ PDF Chat	Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters	1962	T. A. Magness J. B. McGuire	6
+ PDF Chat	Inequalities - Theory of Majorization and Its Applications	1979		6
+	On the theory of testing serial correlation	1948	T. W. Anderson	6
+	The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator	1989	Simo Puntanen George P. H. Styan	6
+	The distribution of quadratic forms in a normal system, with applications to the analysis of covariance	1934	W. G. Cochran John Wishart	6
+	Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor	1997	Geoffrey S. Watson Gülhan Alpargu George P. H. Styan	5
+	Extensions of Samuelson's Inequality	1979	Henry Wolkowicz George P. H. Styan	5
+	On the relative goodness of ordinary least squares estimation in the general linear model	1987	Simo Puntanen	5
+	Inefficiency and correlation	1981	Flavio C. Bartmann Peter Bloomfield	5
+	Some extensions of the Kantorovich inequality and statistical applications	1981	C. G. Khatri C. Radhakrishna Rao	5
+	A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics	1962	C. Radhakrishna Rao	5
+	An Introduction to Multivariate Statistical Analysis	1986	Robb J. Muirhead T. W. Anderson	5
+	Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities	1991	Jerzy K. Baksalary Simo Puntanen	5
+ PDF Chat	How Much Do Gauss-Markov and Least Square Estimates Differ? A Coordinate-Free Approach	1975	Shelby J. Haberman	5
+	On the minimum efficiency of least squares	1975	M. Knott	5
+	A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse	1974	David Carlson Emilie V. Haynsworth Thomas L. Markham	4
+	On some characterizations of the “star” partial ordering for matrices and rank subtractivity	1986	Robert E. Hartwig George P. H. Styan	4
+	RANK ADDITIVITY AND MATRIX POLYNOMIALS	1983	George P. H. Styan Akimichi Takemura	4
+	Two matrix-based proofs that the linear estimator Gy is the best linear unbiased estimator	2000	Simo Puntanen George P. H. Styan Hans‐Joachim Werner	4
+	On the Bounds of the Range of Order Statistics	1971	Douglas M. Hawkins	4
+	The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator	1989	Simo Puntanen George P. H. Styan	4
+	Unified theory of linear estimation	1971	C. Radhakrishna Rao	4
+	A Matrix Formulation on How Deviant an Observation Can Be	1992	Ingram Olkin	4
+	Some comments on several matrix inequalities with applications to canonical correlations: Historical background and recent developments	2002	S.W. Drury Shuangzhe Liu Chang-Yu Lu Simo Puntanen George P. H. Styan	4
+	On a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys	1985	Alastair J. Scott George P. H. Styan	4
+	Some Generalizations of Kantorovich Inequality	1981	C. G. Khatri C. Mallikarjuna Rao	4
+	Reversal of the Lyapunov, Hölder, and Minkowski inequalities and other extensions of the Kantorovich inequality	1964	Albert W. Marshall Ingram Olkin	4
+ PDF Chat	Linear Least Squares Regression	1967	Geoffrey S. Watson	4
+	A note on rank-additivity	1981	Robert E. Hartwig	3
+	Inheriting independence and chi-squaredness under certain matrix orderings	1984	Jerzy K. Baksalary Jan Hauke	3
+	Nonsingularity of the Difference of Two Oblique Projectors	2000	Jürgen Groß Götz Trenkler	3
+	A note on the partial ordering of positive semi-definite matrices	1978	Robert E. Hartwig	3
+	Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings	1990	Jerzy K. Baksalary Simo Puntanen	3
+	The greatest distance between two characteristic roots of a matrix	1959	Alfred Brauer A. C. Mewborn	3
+	Parametric Augmentations and Error Structures under which Certain Simple Least Squares and Analysis of Variance Procedures are Also Best	1969	George Zyskind	3
+ PDF Chat	Some metric inequalities in the space of matrices	1955	Ky Fan Alan J. Hoffman	3
+ PDF Chat	Relative hermitian matrices	1961	Magnus R. Hestenes	3
+ PDF Chat	Comparison of the Variance of Minimum Variance and Weighted Least Squares Regression Coefficients	1963	Gene H. Golub	3