Jerzy Baksalary

Jerzy Kazimierz Baksalary (25 June 1944 – 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.

Biography

Early life and education (1944 – 1988) Baksalary was born in Poznań, Poland on 25 June 1944. He received a Habilitation in 1984, also from Adam Mickiewicz University, where his Habilitationsschrift was also on linear statistical models. in Canada from 9 to 10 June 2005.

Research In 1979, Baksalary and Radosław 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. (Here, the notation , is adopted for any matrix M.

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 . These include three previously known cases , , or , previously found by Rao and Mitra (1971); and one additional case where and .