Jerzy Kazimierz Baksalary (25 June 1944 â 8 March 2005) was a Polish mathematician who specialized in mathematical statistics and linear algebra. 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.
Baksalary was born in Poznaà Â, Poland on 25 June 1944. From 1969 to 1988, he worked at the Agricultural University of Poznaà Â.
In 1975, Baksalary received a PhD degree from Adam Mickiewicz University in Poznaà Â; his thesis on linear statistical models was supervised by Tadeusz Calià Âski. He received a Habilitation in 1984, also from Adam Mickiewicz University, where his Habilitationsschrift was also on linear statistical models.
In 1988, Baksalary joined the Tadeusz Kotarbià Âski Pedagogical University in Zielona Góra, Poland, being the university's rector from 1990 to 1996. In 1990, he became a "Professor of Mathematical Sciences", a title received from the President of Poland. For the 1989âÂÂ1990 academic year, he moved to the University of Tampere in Finland. Later on, he joined the University of Zielona Góra.
Baksalary died in Poznaà  on 8 March 2005. His funeral was held there on 15 March 2005. There, Calià Âski praised Baksalary for his "contributions to the Poznaà  school of mathematical statistics and biometry".
Memorial events in honor of Baksalary were also held at two conferences after his death:
In 1979, Baksalary and Radosà Âaw Kala proved that the matrix equation has a solution for some matrices X and Y if and only if . (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.
In 1980, he and Kala extended this result to the matrix equation , proving that it can be solved if and only if , where and . (Here, the notation , is adopted for any matrix M.)
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.
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. Similarly, A is below B in the right-star ordering, written , iff and .
In 2000, Jerzy Baksalary and Oskar Maria Baksalary characterized all situations when a linear combination of two idempotent matrices can itself be idempotent. These include three previously known cases , , or , previously found by Rao and Mitra (1971); and one additional case where and .