Michael Peter Drazin (born 5 June 1929) is a British and American mathematician, working in

noncommutative algebra In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist ''a'' and ''b'' in the ring such that ''ab'' and ''ba'' are different. Equivalently, a ''noncommutative ring'' is a ring that is not a ...

Background

The Drazins (Дразин) were a

Russian Jewish The history of the Jews in Russia and areas historically connected with it goes back at least 1,500 years. Jews in Russia have historically constituted a large religious and ethnic diaspora; the Russian Empire at one time hosted the largest po ...

family who moved to the United Kingdom in the years before

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

. Isaac Drazin founded in 1927 a well-known electrical goods shop in Heath Street,

Hampstead Hampstead () is an area in London, England, which lies northwest of Charing Cross, located mainly in the London Borough of Camden, with a small part in the London Borough of Barnet. It borders Highgate and Golders Green to the north, Belsiz ...

, which existed for over 50 years. Isaac Drazin married Leah Wexler, and had three sons, of whom Michael was the eldest, and

Philip Drazin Philip Gerald Drazin (25 May 1934 – 10 January 2002) was a British mathematician and a leading international expert in fluid dynamics. Biography Drazin was born in East London to Isaac Drazin, who was of Russian-Jewish origin and ran a shop i ...

, also a mathematician, was the youngest, the middle son being David; and died 1 January 1993.

Life

Michael Drazin was born in London on 5 June 1929. His younger brother Philip was educated as a boarder at

St Christopher School St Christopher School is a private day and boarding school in Letchworth Garden City, Hertfordshire, England. Established in 1915 as the Garden City Theosophical School, it has long been a flagship of progressive education. The present name was ...

Letchworth Letchworth Garden City, commonly known as Letchworth, is a town in the North Hertfordshire district of Hertfordshire, England. It is noted for being the first garden city. The population at the time of the 2021 census was 33,990. Letchworth ...

during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. The self-published memoirs of Roger Atkinson, a school friend of Michael (Mike), indicate that Drazin attended

King Alfred School, London The King Alfred School is a co-educational independent day school in Golders Green in North West London. It was founded in London in 1898 by Charles E. Rice, a former teacher at Bedales School '. The school was considered "radical" for its er ...

, located in

, retaining contacts at the school when it was evacuated in wartime to

Royston, Hertfordshire Royston is a town and Civil parishes in England, civil parish in the North Hertfordshire, District of North Hertfordshire and county of Hertfordshire in England. It is situated on the Prime meridian (Greenwich), Greenwich Meridian, which brush ...

; Atkinson was a boarder at St Christopher School, Letchworth from September 1942. In 1946 Atkinson and Drazin visited Paris together. Drazin was a student at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

, graduating B.A. in 1950 and M.A. in 1953. He was awarded a Ph.D. in 1953 for a dissertation ''Contributions to Abstract Algebra'' written with advisers

Robert Rankin Robert Fleming Rankin (born 27 July 1949) is a prolific British author of fantasy comedy, comedic fantasy novels. Born in Parsons Green, London, he started writing in the late 1970s, and first entered the bestsellers lists with ''Snuff Fictio ...

and David Rees. He was a Fellow of

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

from 1952 to 1956, during that period relocating to the United States. In the academic year 1957–8 Drazin was Visiting Lecturer at

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

. In 1958 he began a period at RIAS Inc. (the

Research Institute for Advanced Studies The Baltimore-based Research Institute for Advanced Studies (RIAS), not to be confused with the better-known Institute for Advanced Study in Princeton, New Jersey, was among the several centers for research in the mathematical and physical sciences ...

) in

Baltimore Baltimore is the most populous city in the U.S. state of Maryland. With a population of 585,708 at the 2020 census and estimated at 568,271 in 2024, it is the 30th-most populous U.S. city. The Baltimore metropolitan area is the 20th-large ...

as senior scientist, after which he took a position as associate professor at

Purdue University Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...

in 1962.

Works

Drazin gave his name to a type of

generalized inverse In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inv ...

in ring theory and

semigroup theory In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily the ...

he introduced in 1958, now known as the

Drazin inverse In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix. Let ''A'' be a square matrix. The index of ''A'' is the least nonnegative integer ''k'' such that rank(''A'k''+1) = rank(''A'k'' ...

. It was later extended to contexts in

operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operato ...

. While at RIAS, Drazin worked with

Emilie Virginia Haynsworth Emilie Virginia Haynsworth (June 1, 1916 – May 4, 1985) was an American mathematician at Auburn University who worked in linear algebra and matrix theory. She gave the name to Schur complements and is the namesake of the Haynsworth inertia addit ...

, then at the

National Bureau of Standards The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

, within its

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

program. He also worked with the metallurgist Henry Martin Otte of RIAS, and they published a book of crystallographic tables.

References

External links

Home page at Purdue

List of publications at www.math.purdue.edu
* Living people 1929 births 20th-century American mathematicians 20th-century British mathematicians 21st-century American mathematicians 21st-century British mathematicians Alumni of the University of Cambridge English people of Russian-Jewish descent Fellows of Trinity College, Cambridge Mathematicians from London People educated at King Alfred School, London People from Stepney Purdue University faculty {{US-mathematician-stub

Background

Life

Works

See also

References

External links