Heinz Neudecker (October 3, 1933 – December 5, 2017) was an Austrian-Dutch econometrician and statistician, recognised as a pioneering figure and a ‘founding father’ of matrix differential calculus. Liu, S., Trenkler, G., Kollo, T., von Rosen, D. & Baksalary, O.M. Professor Heinz Neudecker and matrix differential calculus, Statistical Papers (2024) 65:2605–2639. https://www.researchgate.net/publication/374417466_Professor_Heinz_Neudecker_and_matrix_differential_calculusCarles M.Cuadras, In memoriam: Heinz Neudecker (1933-2017), Statistics and Operations Research Transactions (SORT), Vol. 42, no. 2, July-December 2018 https://www.idescat.cat/serveis/biblioteca/docs/bib/publicacions/r00262018v422.pdf
Biography
Heinz Neudecker was born on 3 October 1933, in The Hague, in the Netherlands. In 1961, Heinz married Erica Engels, and they had three children: Ilia, Hannah, and Franz. Heinz Neudecker passed away in Haarlem on 5 December 2017, at the age of 84.Death notice, Volkskrant, 10 December, 2017.An obituary published in December, 2017, written by Professor Peter Boswijk, University of Amsterdam, is no longer accessible.http://www.uva.nl/shared-content/faculteiten/nl/faculteit-economie-en-bedrijfskunde/nieuws/2017/12/in-memoriam-heinz-neudecker.htmlhttps://www.noordhollandsdagblad.nl/incoming/eigenzinnige-hoogleraar-in-korte-broek/9994324.html
Education and Professional career 1959 Degree in Economics (drs., equivalent to a master’s degree), Economische Hogeschool in Rotterdam (later renamed Erasmus University). 1959–1964: Researcher at Landbouw-Economisch Instituut, The Hague, Netherlands 1964–1969: Lector/Senior Lecturer, University of Birmingham, UK 1967: Ph.D., University of Birmingham, UK; Dissertation: Matrix Methods for Econometric ResearchNeudecker, H. (1967). Matrix methods for econometric research (Doctoral dissertation, University of Birmingham). Retrieved from etheses.bham.ac.uk/id/reprint/13211/ 1969–1971: Visiting Professor of Economics, Middle East Technical University (Orta Doğu Teknik Üniversitesi), Ankara, Turkey 1971–1972: Professor of Econometrics, Vrije Universiteit Brussel, Belgium (later continued as a special part-time professorship) 1972–1998: Professor of Econometrics, University of Amsterdamhttps://albumacademicum.uva.nl/id/id002413 1979 (September 1) – 1980 (July 31): Fellow at the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), where he conducted research on matrix differential calculus, (0,1) matrices, and variance matrix estimation in normal regression.
Heinz’s final speech upon retirement from the University of Amsterdam was titled Afscheid van dierenboerderij (Goodbye to the Animal Farm), which was published in a limited paper edition by UvA in 1998.Neudecker, H., & Neudecker, H. Archief Heinz Neudecker. International Institute for Social History, Amsterdam, https://hdl.handle.net/10622/ARCH01003 As a professor emeritus, Heinz remained actively engaged in the international fields of statistics and matrix differential calculus. He continued to supervise young academics, publish papers in leading journals, and speak at conferences around the world until 2015.Carles M.Cuadras, In memoriam: Heinz Neudecker (1933-2017), Statistics and Operations Research Transactions (SORT), Vol. 42, no. 2, July-December 2018 https://www.idescat.cat/serveis/biblioteca/docs/bib/publicacions/r00262018v422.pdf
In 2000, several of his international colleagues honoured his contributions to multivariate statistical analysis with a commemorative publication: Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker (edited by R. D. H. Heijmans, D. S. G. Pollock, and A. Satorra).
The book Matrix Differential Calculus with Applications in Statistics and Econometrics, co-authored by Heinz Neudecker and Jan Magnus, has been published in three editions (Wiley, 1988, 1999, 2019). It remains an essential reference for scholars and students worldwide. The book is widely recognised for its rigorous treatment of matrix calculus and its applications in econometrics and statistics, shaping the fields and advancing research in multivariate analysis.
Pioneer of matrix differential calculus Carles M. Cuadras, in his In memoriam, states the following: 'With more than 139 publications indexed in the ISI web of knowledge, Neudecker reshaped the field of matrix algebra for econometrics and multivariate analysis. He is the author (with one of his Ph.D. students, Jan Magnus) of the most influential book in the area, Matrix Differential Calculus with Applications in Statistics and Econometrics, with first edition in 1988 and a revised edition in 1991. The second edition was published in 1999.'Carles M.Cuadras, In memoriam: Heinz Neudecker (1933-2017), Statistics and Operations Research Transactions (SORT), Vol. 42, no. 2, July-December 2018 https://www.idescat.cat/serveis/biblioteca/docs/bib/publicacions/r00262018v422.pdf
Further, Heinz Neudecker's pioneering role and continuing influence in matrix differential calculus is borne out by the following facts:
His doctoral dissertation, Matrix methods for economic research (1967), is still accessed on the internet.http://etheses.bham.ac.uk/id/eprint/13211
In the field of matrix differential calculus, Heinz Neudecker is considered by many scholars as its founding father, as stated in Liu et al. 2024.see ref. 1 This can also be inferred from the many citations of his work:The second edition of Matrix Differential Calculus has been quoted 6327 times;Google Scholar, accessed 26 August 2025 Neudecker, H. (1969), Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products, Journal of the American Statistical Association, 64(327), 953–963, was quoted 193 times,Google Scholar, accessed 26 August, 2025 most recently in Mahdi, E., & Fisher, T. J. (2022). Bootstrapping a powerful mixed portmanteau test for time series. Journal of Applied Statistics, 51(2), 230–255.
A very personal reference to Neudecker’s influence can be found in the introduction Götz Trenkler wrote in one of his papers: ‘A few years ago, Heinz Neudecker sent me a complimentary copy of his paper entitled Mathematical properties of the variance of the multinomial distribution. On the first page was the handwritten message: “Lieber Herr Trenkler, vielleicht interessiert Sie diese Arbeit! Ihr HN.”Translation from the German: Dear Mr Trenkler, maybe this work will be of interest to you! Yours, HN. In fact, I found this paper, Neudecker (1995), so impressive that it motivated me to work on the same topic, namely the covariance of the multinomial distribution and related matrix theory. Of course, the reader will recognise the use of some of Neudecker’s favourite tools and tricks in the results below.’Trenkler, G. (2000). On a Generalisation of the Covariance Matrix of the Multinomial Distribution. In: Heijmans, R.D.H., Pollock, D.S.G., Satorra, A. (eds) Innovations in Multivariate Statistical Analysis. Advanced Studies in Theoretical and Applied Econometrics, vol 36. Springer, Boston, MA.
· Neudecker’s work is also applied in several scientific disciplines that employ statistical analysis, like biometrics, sustainability sciences and geophysics.Bunsen, J., & Finkbeiner, M. (2023). An Introductory Review of Input-Output Analysis in Sustainability Sciences Including Potential Implications of Aggregation. Sustainability, 15(1), 46, citing Neudecker, H. (1970). Aggregation in input-output analysis: an extension of Fisher's method. Econometrica: Journal of the Econometric Society, 921-926;Erik W. Grafarend, Silvelyn Zwanzig, Joseph L. Awange, Applications of Linear and Nonlinear Models - Fixed Effects, Random Effects, and Total Least Squares, Springer Geophysics , 2022 citing Neudecker, H. (1977). Bounds for the Bias of the Least Squares Estimator of σ 2 in the Case of a First-Order Autoregressive Process (Positive Autocorrelation). Econometrica: Journal of the Econometric Society, 1257-1262.
Politics
Heinz had a lifelong commitment to improving society through political activism. During his university studies in Rotterdam, he was a member of the Democratic Socialist student society Politeia, one of a 'gang of four' econometrics students pushing the organisation to a more radical course. According to his lifelong friend, Arie van der Zwan, 'Heinz was the most intellectual of the three of us’, the third person mentioned being Henk Lange. An article on the group in the periodical HP in 1984, refers to Heinz Neudecker as "a somewhat thoughtful 'ideologist' in the background".Socialistische Jeugd – De ramp van het ziekenfonds-socialisme, HP, 21 April, 1984, p. 24-28. A photograph in this article shows the three of them at a public meeting, with a book on Elementary Statistical Analysis and a reader on Karl Marx just visible on a table in front.Private interview with Arie van der Zwan, 27 September, 2023.. Heinz was also a member of the linked to the Social Democratic Party's youth organisation Nieuwe Koers,Neudecker, H., & Neudecker, H. Archief Heinz Neudecker. International Institute for Social History, Amsterdam, https://hdl.handle.net/10622/ARCH01003 where he met Erica, his future wife. In the early 1960s, he published analyses on political subjects in Maatstaf and Gard Sivik and campaigned for human rights in countries like Algeria, Vietnam,Two posters announcing demonstrations in London in 1967 and 1968, respectively, are kept in his personal archive at the International Institute Of Social History, https://hdl.handle.net/10622/N30051003119655?locatt=view:level3 and https://hdl.handle.net/10622/N30051003119663?locatt=view:level3 and TurkeyA brochure written by Heinz Neudecker, Turkije: Repressie, liberalisering, repressie, published around 1974, is in the collection of the International Institute for Social History, Amsterdam, https://hdl.handle.net/10622/1A591DCE-56FA-463F-A870-8AA3FF0AB237. Having become disenchanted with Social Democracy, Heinz became involved in the Green Movement in the early 1970s. He started a local Green party in his town of Schagen and served as a member of the municipal council for several years.https://hdl.handle.net/10622/E52F9F57-22FE-41D6-AF5F-B199D0B57B6Chttps://www.noordhollandsdagblad.nl/incoming/eigenzinnige-hoogleraar-in-korte-broek/9994324.htmlhttps://noordkopcentraal.nl/heinz-neudecker-overleden/
Contributor and editor to Gard Sivik and Maatstaf, 1960s
Heinz Neudecker was one of the main contributors of Gard Sivik, an experimental Flemish-Dutch journal, and also published articles for it in the early 60s.Gard Sivik Jaargang 6 (1962) https://www.dbnl.org/tekst/_gar001196201_01/_gar001196201_01_0049.php Between 1963 and 1966, he contributed to Maatstaf, a literary and political journal, where he wrote about significant contemporary issues such as the Cold War, the Vietnam War, and his visit to Russia. His involvement in these discussions reflected his broader interest in global political dynamics during a time of great tension. Additionally, from 1965 to 1966, Heinz served as a guest editor for Maatstaf, further showcasing his engagement with both literary and political discourse.
Published academic works