Rajendra Bhatia | Academic Influence

Rajendra Bhatia's AcademicInfluence.com Rankings

Rajendra Bhatia

Mathematics

#610

World Rank

#1142

Historical Rank

Linear Algebra

#3

World Rank

#3

Historical Rank

Measure Theory

#1038

World Rank

#1336

Historical Rank

mathematics Degrees

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Mathematics

Why Is Rajendra Bhatia Influential?

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According to Wikipedia, Rajendra Bhatia is an Indian mathematician, author, and educator. He is currently a professor of mathematics at Ashoka University located in Sonipat, Haryana ,India. Education He studied at the University of Delhi, where he completed his BSc degree in physics and MSc degree in mathematics, and moved to the Indian Statistical Institute, Kolkata, where he completed his Ph.D. in 1982 under the probabilist K. R. Parthasarathy.

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Rajendra Bhatia's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Matrix Analysis (1996) (1565)
Positive Definite Matrices (2019) (1155)
How and Why to Solve the Operator Equation AX−XB = Y (1997) (270)
Riemannian geometry and matrix geometric means (2006) (245)
Riemannian geometry for EEG-based brain-computer interfaces; a primer and a review (2017) (243)
A Better Bound on the Variance (2000) (206)
On the Bures–Wasserstein distance between positive definite matrices (2017) (181)
On the singular values of a product of operators (1990) (172)
Perturbation Bounds for Matrix Eigenvalues (2007) (163)
More matrix forms of the arithmetic-geometric mean inequality (1993) (163)
Perturbation of spectral subspaces and solution of linear operator equations (1983) (147)
Notes on matrix arithmetic–geometric mean inequalities (2000) (132)
Infinitely Divisible Matrices (2006) (118)
Orthogonality of matrices and some distance problems (1999) (113)
Matrix Information Geometry (2012) (102)
A CAUCHY-SCHWARZ INEQUALITY FOR OPERATORS WITH APPLICATIONS (1995) (94)
Norm inequalities for partitioned operators and an application (1990) (87)
On the exponential metric increasing property (2003) (86)
Positive Definite Functions and Operator Inequalities (2000) (83)
Interpolating the arithmetic-geometric mean inequality and its operator version (2006) (83)
Monotonicity of the matrix geometric mean (2012) (81)
The logarithmic mean (2008) (72)
The matrix arithmetic-geometric mean inequality revisited (2008) (68)
Linear Algebra to Quantum Cohomology: The Story of Alfred Horn's Inequalities (2001) (60)
Matrix factorizations and their perturbations (1994) (57)
Norm Inequalities for Positive Operators (1998) (53)
An extremal problem in Fourier analysis with applications to operator theory (1989) (51)
Maps on matrices that preserve the spectral radius distance (1999) (49)
On symplectic eigenvalues of positive definite matrices (2015) (48)
Mean matrices and infinite divisibility (2007) (47)
Some inequalities for positive linear maps (2012) (47)
Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix (1990) (47)
Comparing a Matrix to its Off-Diagonal Part (1989) (41)
More Operator Versions of the Schwarz Inequality (2000) (41)
Norm inequalities related to the matrix geometric mean (2012) (40)
Some inequalities for norm ideals (1987) (39)
Clarkson Inequalities with Several Operators (2004) (39)
Loewner matrices and operator convexity (2009) (38)
First and second order perturbation bounds for the operator absolute value (1994) (38)
A bound for the spectral variation of a unitary operator (1984) (37)
The Hoffman-Wielandt inequality in infinite dimensions (1994) (37)
Approximate Isometries on Euclidean Spaces (1997) (34)
Perturbation inequalities for the absolute value map in norm ideals of operators (1988) (34)
Cartesian decompositions and Schatten norms (2000) (33)
ANALYSIS OF SPECTRAL VARIATION AND SOME INEQUALITIES (1982) (31)
Matrix versions of the Hellinger distance (2019) (31)
Noncommutative geometric means (2006) (30)
On the Clarkson-McCarthy inequalities (1988) (30)
Variation of Grassman powers and spectra (1981) (30)
The Riemannian Mean of Positive Matrices (2013) (29)
Pinching, Trimming, Truncating, and Averaging of Matrices (2000) (29)
Some inequalities for commutators and an application to spectral variation (1990) (28)
Differentiation of Operator Functions and Perturbation Bounds (1998) (26)
BY POSITIVE MATRICES (25)
Some norm inequalities for matrix means (2016) (24)
Higher order derivatives and perturbation bounds for determinants (2009) (24)
Eigenvalue inequalities associated with the cartesian decomposition (1987) (23)
A note on the Lyapunov equation (1997) (23)
Short normal paths and spectral variation (1985) (23)
Variation of real powers of positive operators (1994) (21)
Compact operators whose real and imaginary parts are positive (2000) (20)
Some inequalities for communtators and an application to spectral variation (1990) (19)
Partial traces and entropy inequalities (2003) (19)
Min Matrices and Mean Matrices (2011) (19)
Perturbation bounds for the operator absolute value (1995) (19)
Variation of symmetric tensor powers and permanents (1984) (18)
The singular values of A+B and A+iB (2009) (18)
Commutators, pinchings, and spectral variation (2008) (18)
Positive Linear Maps and Spreads of Matrices (2014) (18)
Inequalities for the Wasserstein mean of positive definite matrices (2018) (17)
Frechet derivatives of the power function (2000) (17)
Variation of the Unitary Part of a Matrix (1994) (17)
On the rate of change of spectra of operators. II (1979) (17)
Notes on Functional Analysis (2009) (16)
The operator equation ∑ i = 0 n A n - i XB i = Y (2009) (16)
Trace inequalities for products of positive definite matrices (2014) (16)
Positivity Preserving Hadamard Matrix Functions (2007) (16)
Variation of induced linear operators (2002) (16)
Unitary invariance and spectral variation (1987) (15)
Some Inequalities for Norms of Commutators (1997) (15)
Strong convexity of sandwiched entropies and related optimization problems (2018) (15)
Positive linear maps and spreads of matrices-II (2016) (13)
Inertia of the matrix $[(p_i+p_j)^r]$ (2015) (13)
Generalized Lyapunov Equations and Positive Definite Functions (2005) (12)
Positivity and conditional positivity of Loewner matrices (2010) (12)
NORM INEQUALITIES FOR OPERATORS WITH POSITIVE REAL PART (2003) (12)
Positive Linear Maps and the Lyapunov Equation (2002) (11)
Derivations, derivatives and chain rules (1999) (11)
Pinchings and Norms of Scaled Triangular Matrices (2002) (11)
Some inequalities for commutators and an application to spectral variation. II (1997) (10)
On perturbations of matrix pencils with real spectra. II (1996) (10)
A unitary analogue of Kato's theorem on variation of discrete spectra (1988) (10)
On some perturbation inequalities for operators (1988) (10)
The distance between the eigenvalues of Hermitian matrices (1986) (9)
A Generalization of the Hoffman-Wielandt Theorem (1993) (9)
An interpolating family of means (2012) (9)
Infinite Divisibility of GCD Matrices (2008) (8)
Perturbation Bounds for Matrix Eigenvalues (Classics in Applied Mathematics) (2007) (8)
Corners of normal matrices (2006) (8)
Inertia of Loewner Matrices (2015) (8)
Derivatives of tensor powers and their norms (2011) (8)
On some positive definite functions (2014) (7)
The Weak Topology (2009) (7)
Perturbation of extended enumerations of eigenvalues (1999) (7)
Mean matrices and conditional negativity (2016) (7)
A Schur-Horn theorem for symplectic eigenvalues (2020) (6)
A Henrici theorem for joint spectra of commuting matrices (1993) (6)
On the joint spectral radius of commuting matrices (1995) (6)
Operator Monotone and Operator Convex Functions (1997) (6)
Eigenvalues of symmetrizable matrices (1998) (6)
Approximation by positive operators (1992) (6)
The matrix geometric mean (2011) (6)
Distance between commuting tuples of normal operators (1998) (6)
A softer, stronger Lidskii theorem (1989) (6)
A Review of Linear Algebra (1997) (5)
Relations of Linking and Duality between Symmetric Gauge Functions (1994) (5)
INERTIA OF THE MATRIX (2013) (5)
On the variation of permanents (1990) (5)
FOURIER SERIES (2005) (5)
Higher Order Logarithmic Derivatives of Matrices in the Spectral Norm (2003) (5)
Symmetries and Variation of Spectra (1992) (5)
The bipolar decomposition (2013) (4)
Analysis, Geometry and Probability (1996) (4)
Plenary lectures and ceremonies (2010) (4)
Normal approximants to binormal operators (1991) (4)
Variational principles for symplectic eigenvalues (2020) (4)
Distance between Hermitian operators in Schatten classes (1996) (4)
On weighted lowdin orthogonalization (1986) (4)
Eigenvalues of AB and BA (2002) (4)
Modulus of continuity of the matrix absolute value (2010) (3)
Procrustes problems in Riemannian manifolds of positive definite matrices (2019) (3)
Spectral variation bounds for diagonalisable matrices (1997) (3)
An old question asked in a new context presents strange aspects (2006) (3)
Perturbation theorems for Hermitian elements in Banach algebras (1999) (3)
Some inequalities for eigenvalues and symplectic eigenvalues of positive definite matrices (2019) (3)
Spectral variation, normal matrices, and finsler geometry (2007) (3)
The work of the fields medallists: 1998 (1999) (3)
On Joint Eigenvalues of Commuting Matrices (1996) (3)
Fourier Series: A Brief Bibliography (2005) (3)
A key inequality for functions of matrices (2001) (3)
The space of unordered tuples of complex numbers (1983) (3)
Particle systems and their large deviations (2012) (2)
A Szegő type theorem and distribution of symplectic eigenvalues (2020) (2)
Approximate isometrics on Euclidean spaces (1997) (2)
Correction to: Matrix versions of the Hellinger distance (2019) (2)
Review of matrix perturbation theory: by G.W. Stewart and Ji-guang Sun☆ (1992) (2)
Perturbation of Matrix Functions (1997) (2)
Connected at Infinity: A Selection of Mathematics by Indians (2003) (2)
Concavity of certain functions of matrices (1985) (2)
Algebraic geometry solves an old Matrix problem (1999) (2)
Variational Principles for Eigenvalues (1997) (2)
Positivity properties of the matrix (i+j)i+j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left[(i+j)^{i+j}\right]} (2014) (2)
Preface to the 12th ILAS Conference Proceedings, Regina 2005 (2007) (1)
Majorisation and Doubly Stochastic Matrices (1997) (1)
Approximation problems in the Riemannian metric on positive definite matrices (2014) (1)
Positivity properties of the matrix $${\left[(i+j)^{i+j}\right]}$$(i+j)i+j (2014) (1)
On residual bounds for eigenvalues (1992) (1)
The Future of Mathematics Publishing (2015) (1)
Independence of Judiciary and the Appointment of Judges (1999) (1)
A Conversation with S. R. S. Varadhan (2008) (1)
Orthogonalisation of vectors (2000) (1)
Fourier Series: Preface (2005) (1)
Correction to: Matrix versions of the Hellinger distance (2019) (0)
Extensions of the Schur majorisation inequalities (2022) (0)
Limit theorems, review articles (2012) (0)
Some Special Operators in Hilbert Space (2009) (0)
SHORT NORMAL PATHS AND SPECTRAL VARIATION1 (2010) (0)
13. Related Topics (2007) (0)
Fourier Series: Heat Conduction and Fourier Series (2005) (0)
The Spectral Theorem -I (2009) (0)
Chapter Four. Matrix Means (2009) (0)
Chapter Two. Positive Linear Maps (2009) (0)
Title Some Problems in Fourier Analysis and Matrix Theory(Recent (2018) (0)
Fourier Series: Some Applications (2005) (0)
PERTURBATION BOUNDS FOR EIGENVALUES : A SURVEY (1986) (0)
Fourier Series: Convergence of Fourier Series (2005) (0)
Vibration and Eigenvalues (2010) (0)
Matrix versions of the Hellinger distance (2019) (0)
A Selection of Matrix Inequalities (1997) (0)
Convolutions (2017) (0)
Vibrations and eigenvalues (2017) (0)
Chapter Three. Completely Positive Maps (2009) (0)
Preface: Special volume of Electronic Journal of Linear Algebra dedicated to Professor Ravindra B. Bapat (2015) (0)
2. Singular Values and Norms (2007) (0)
David Hilbert (1999) (0)
The numerical radius and positivity of block matrices (2022) (0)
Postscripts and References (2007) (0)
Compact Operators and Invariant Subspaces (2009) (0)
Monotonicity of the matrix geometric mean (2011) (0)
12. Arbitrary Perturbations of Constrained Matrices (2007) (0)
Some Problems in Fourier Analysis and Matrix Theory(Recent Developments in Linear Operator Theory and its Applications) (2005) (0)
Vibrations and eigenvalues (2017) (0)
Connected at Infinity II (2013) (0)
Perturbation by unbounded operators (1978) (0)
Triangularisation of a matrix (2000) (0)
Subdivision of the Spectrum (2009) (0)
Spectra of Normal Operators (2009) (0)
PDE, SDE, diffusions, random media (2012) (0)
7. Singular Values and Norms (2007) (0)
Special issue dedicated to Roger Horn (2007) (0)
The Second Dual and the Weak* Topology (2009) (0)
Higher Order Logarithmic Derivatives of Matrices (2002) (0)
Square Roots and the Polar Decomposition (2009) (0)
Calculus of operator functions (2007) (0)
Fourier Series: Odds and Ends (2005) (0)
The Spectrum of a Compact Operator (2009) (0)
11. The General Spectral Variation Problem (2007) (0)
The Spectral Theorem -III (2009) (0)
The Spectral Theorem -II (2009) (0)
The Hahn-Banach Theorem (2009) (0)
8. Spectral Variation of Hermitian Matrices (2007) (0)
TRICKS AND TECHNIQUE WITH OOPS (OIL ON PAPER SCHOOL) (2019) (0)
The Resolvent and The Spectrum (2009) (0)
On some positive definite functions (2015) (0)
Chapter Six. Geometry of Positive Matrices (2009) (0)
10. Spectral Variation of Diagonalizable Matrices (2007) (0)
Sensitivity of the Solutions of Some Matrix Equations (1997) (0)
Analysis, geometry and probability : essays in honour of K.R. Parthasarathy (1996) (0)
Triangularization of a matrix (2000) (0)
Chapter One. Positive Matrices (2009) (0)
New Banach Spaces from Old (2009) (0)
Linear Algebra and Analysis Masterclasses (2016) (0)
Perturbation of Spectral Subspaces of Normal Matrices (1997) (0)
Eigenvalues and diagonal elements (2022) (0)
Spectral Variation of Normal Matrices (1997) (0)
The unexpected appearance of Pi in diverse problems (2003) (0)
Fourier Series: Convergence in L 2 and L 1 (2005) (0)
In the matrix mould : expository articles by Rajendra Bhatia (2013) (0)
3. Spectral Variation of Hermitian Matrices (2007) (0)
ELA DERIVATIVES OF TENSOR POWERS AND THEIR NORMS (2019) (0)
Fourier Series: A Note on Normalisation (2005) (0)
Fourier Series by Rajendra Bhatia (2005) (0)
Chapter Five. Positive Definite Functions (2009) (0)
Understanding the dynamics of adoption decisions and their poverty impacts (2018) (0)
The Open Mapping Theorem (2009) (0)
Isometries and Linearity (2022) (0)
The Uniform Boundedness Principle (2009) (0)
A survey of Heydar Radjavi (2004) (0)
Fourier Series: A History of Fourier Series (2005) (0)
Spectral Variation of Nonnormal Matrices (1997) (0)

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What Schools Are Affiliated With Rajendra Bhatia?

Rajendra Bhatia is affiliated with the following schools:

Ashoka University

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