Jerzy Kazimierz Baksalary (25 June 1944 – 8 March 2005) was a Polish mathematician who specialized in mathematical statistics and linear algebra.[1] In 1990 he was appointed professor of mathematical sciences. He authored over 170 academic papers published and won one of the Ministry of National Education awards.[2]
Jerzy Baksalary | |
---|---|
Baksalary in 1993 | |
Born | |
Died | 8 March 2005 Poznań, Poland | (aged 60)
Alma mater | Adam Mickiewicz University |
Academic career | |
Discipline | Mathematics |
Sub-discipline | Linear algebra Mathematical statistics |
Institutions | University of Tampere University of Zielona Góra |
Biography
editEarly life and education (1944 – 1988)
editBaksalary was born in Poznań, Poland on 25 June 1944.[1] From 1969 to 1988, he worked at the Agricultural University of Poznań.[1]
In 1975, Baksalary received a PhD degree from Adam Mickiewicz University in Poznań; his thesis on linear statistical models was supervised by Tadeusz Caliński.[1][3] He received a Habilitation in 1984, also from Adam Mickiewicz University, where his Habilitationsschrift was also on linear statistical models.[1]
Career (1988 – 2005)
editIn 1988, Baksalary joined the Tadeusz Kotarbiński Pedagogical University in Zielona Góra, Poland, being the university's rector from 1990 to 1996.[1] In 1990, he became a "Professor of Mathematical Sciences", a title received from the President of Poland.[1] For the 1989–1990 academic year, he moved to the University of Tampere in Finland.[1] Later on, he joined the University of Zielona Góra.[1]
2005 death and legacy
editBaksalary died in Poznań on 8 March 2005.[1][3] His funeral was held there on 15 March 2005.[1][3] There, Caliński praised Baksalary for his "contributions to the Poznań school of mathematical statistics and biometry".[1]
Memorial events in honor of Baksalary were also held at two conferences after his death:[1]
- The 14th International Workshop on Matrices and Statistics, held at Massey University in New Zealand from 29 March to 1 April 2005.
- The Southern Ontario Matrices and Statistics Days, held at the University of Windsor[4] in Canada from 9 to 10 June 2005.
Research
editIn 1979, Baksalary and Radosław Kala proved that the matrix equation has a solution for some matrices X and Y if and only if .[5] (Here, denotes some g-inverse of the matrix A.) This is equivalent to a 1952 result by W. E. Roth on the same equation, which states that the equation has a solution iff the ranks of the block matrices and are equal.[5]
In 1980, he and Kala extended this result to the matrix equation , proving that it can be solved if and only if , where and .[6]: 146 (Here, the notation , is adopted for any matrix M.[6]: 146 )
In 1981, Baksalary and Kala proved that for a Gauss-Markov model , where the vector-valued variable has expectation and variance V (a dispersion matrix), then for any function F, a best linear unbiased estimator of which is a function of exists iff . The condition is equivalent to stating that , where denotes the rank of the respective matrix.[7]
In 1995, Baksalary and Sujit Kumar Mitra introduced the "left-star" and "right-star" partial orderings on the set of complex matrices, which are defined as follows. The matrix A is below the matrix B in the left-star ordering, written , iff and , where denotes the column span and denotes the conjugate transpose.[8]: 76 Similarly, A is below B in the right-star ordering, written , iff and .[8]: 76
In 2000, Jerzy Baksalary and Oskar Maria Baksalary characterized all situations when a linear combination of two idempotent matrices can itself be idempotent.[9] These include three previously known cases , , or , previously found by Rao and Mitra (1971); and one additional case where and .[9]
References
edit- ^ a b c d e f g h i j k l m Baksalary, Oskar Maria; Styan, George P. H. (2005-11-15). "Some comments on the life and publications of Jerzy K. Baksalary (1944–2005)". Linear Algebra and Its Applications. Tenth Special Issue (Part 2) on Linear Algebra and Statistics. 410: 3–53. doi:10.1016/j.laa.2005.08.011. ISSN 0024-3795.
- ^ "Biografia w „Głosie Uczelnianym Uniwersytetu Zielonogórskiego"" (PDF). www.uz.zgora.pl (in Polish). Archived from the original (PDF) on 2012-09-11. Retrieved 2018-11-21.
- ^ a b c Baksalary, Oskar Maria; Styan, George P.H. (2005). "Jerzy K. Baksalary (1944–2005) and his contributions to Image" (PDF). Image. 34: 14–15.
- ^ "Southern Ontario Matrices and Statistics Days Program" (PDF). homepages.tuni.fi. 2005.
- ^ a b Baksalary, J.K.; Kala, R. (June 1979). "The matrix equation AX − YB = C". Linear Algebra and its Applications. 25: 41–43. doi:10.1016/0024-3795(79)90004-1.
- ^ a b Baksalary, J.K.; Kala, R. (April 1980). "The matrix equation AXB+CYD=E". Linear Algebra and its Applications. 30: 141–147. doi:10.1016/0024-3795(80)90189-5.
- ^ Baksalary, J. K.; Kala, R. (July 1981). "Linear Transformations Preserving Best Linear Unbiased Estimators in a General Gauss-Markoff Model". The Annals of Statistics. 9 (4): 913–916. doi:10.1214/aos/1176345533. ISSN 0090-5364.
- ^ a b Baksalary, Jerzy K.; Mitra, Sujit Kumar (1991-04-15). "Left-star and right-star partial orderings". Linear Algebra and its Applications. 149: 73–89. doi:10.1016/0024-3795(91)90326-R. ISSN 0024-3795.
- ^ a b Baksalary, Jerzy K.; Baksalary, Oskar Maria (December 2000). "Idempotency of linear combinations of two idempotent matrices". Linear Algebra and its Applications. 321 (1–3): 3–7. doi:10.1016/s0024-3795(00)00225-1. ISSN 0024-3795.