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I am looking for books on matrices that are perhaps lesser known than the usual suspects (some of which I list below).. Non-english books are welcome (this question is partly motivated by a book on inequalities that I saw some time ago that was in German and now which I cannot find).

Books dealing with inequalities on partitioned matrices and also with strong ties to statistics and covariance matrices would be appreciated.

Generally looking for books that may contain facts etc that are not in every other matrix analysis book and perhaps some non-English books that contain a different perspective.

(There are a couple of other questions similar to this but the list of recommendations were average/standard and many of them focused on linear algebra whereas I am mainly interested in matrix properties and more obscure references).

Some usual suspects:

-Matrix Mathematics: Theory, Facts, and Formulas by Dennis S. Bernstein

I find this first one really comprehensive. This is really along the lines I am thinking also. The German book I cannot find was in the spirit of this first one.

  • Matrix Analysis by Roger A. Horn and Charles R. Johnson
  • Matrix Analysis (Graduate Texts in Mathematics) by Rajendra Bhatia
  • Topics in Matrix Analysis by Roger A. Horn and Charles R. Johnson
  • Matrix Computations by Gene H. Golub and Charles F. van Van Loan
  • Matrix Analysis for Statistics by James R. Schott
  • Matrix Algebra From a Statistician's Perspective by David A. Harville
  • Matrix Differential Calculus with Applications in Statistics and Econometrics by Jan R. Magnus and Heinz Neudecker
  • Introduction to Matrix Analysis by Richard Bellman
  • Linear Matrix Inequalities in System and Control Theory by Stephen Boyd, Laurent El Ghaoui, Eric Feron and Venkataramanan Balakrishnan
  • Inequalities: Theory of Majorization and Its Applications by Albert W. Marshall, Ingram Olkin and Barry C. Arnold
  • A Survey of Matrix Theory and Matrix Inequalities by Marvin Marcus, Henryk Minc

There is also the Matrix Cookbook but that has a lot of errors and surprisingly does not cover a lot of inequalities/identities.

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2 Answers 2

Gantmacher, Felix (1959), Theory of matrices, AMS Chelsea publishing

Peter Lancaster, Miron Tismenetsky The Theory of Matrices: With Applications, Academic Press, 1985

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Some lesser known books complementing the list above:

THE SCHUR COMPLEMENT AND ITS APPLICATIONS by FUZHEN ZHANG Springer

Jacobians of matrix functions and functions of matrix argument by A M Mathai (world scientific)

Quadratic forms in random variables by A M Mathai , Serge B Provost . CRC press.

Aspects of Multivariate Statistical Theory by Robb J Muirhead, Wiley.

Positive Definite Matrices by Rajendra Bhatia Princeton University Press

SPECIAL MATRICES OF MATHEMATICAL PHYSICS STOCHASTIC, CIRCULANT AND BELL MATRICES by R. ALDROVANDI (world scientific)

Generalized Inverses Theory and Applications (second edition) by Adi Ben-Israel and Thomas N E Greville Springer

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