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] Baksalary 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] In 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] Baksalary 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] In 1979, Baksalary and Radosław Kala proved that the matrix equation

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

[5] In 1980, he and Kala extended this result to the matrix equation

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

The condition is equivalent to stating that

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.

denotes the column span and

denotes the conjugate transpose.

[8]: 76  Similarly, A is below B in the right-star ordering, written

[8]: 76 In 2000, Jerzy Baksalary and Oskar Maria Baksalary characterized all situations when a linear combination

[9] These include three previously known cases

, previously found by Rao and Mitra (1971); and one additional case where