Max Atkin Woodbury (1917–2010) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was born in St George, Utah to Angus Munn Woodbury and Grace (Atkin) Woodbury. He had three brothers and two sisters, including the biologists Dixon Miles Woodbury and John Walter Woodbury.

Career

He received his Bachelor of Science from the

University of Utah The University of Utah (the U, U of U, or simply Utah) is a public university, public research university in Salt Lake City, Utah, United States. It was established in 1850 as the University of Deseret (Book of Mormon), Deseret by the General A ...

in 1939, Master of Science from the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

in 1941 and metrology at

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

. He obtained his

doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

at the

in 1948 advised by

Arthur Herbert Copeland Arthur Herbert Copeland (June 22, 1898 Rochester, New York – July 6, 1970) was an American mathematician. He graduated from Harvard University in 1926 and taught at Rice University and the University of Michigan. His main interest was in the fou ...

. His dissertation was entitled

Probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

and

Expected Value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...

s. He was a member of the faculty, University of Michigan 1947-1949,

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in Princeton 1949-1950, member of faculty

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

1950-1952. He moved to be an associate professor in statistics at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

from 1952-1954. After a brief leave at the

Office of Naval Research The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...

1954-1956, he became faculty at

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

from 1956-1965, then a professor of computer science and biomathematics at

Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...

. He became an emeritus professor at Duke, but continued to take an active role in research for many years.

Woodbury identity

The

Woodbury matrix identity In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury – says that the inverse of a rank-''k'' correction of some matrix can be computed by doing a rank-''k'' correction to the inverse of the o ...

used in

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

is named after him.Max A. Woodbury, ''Inverting modified matrices'', Memorandum Rept. 42, Statistical Research Group, Princeton University, Princeton, NJ, 1950, 4pp The related

Sherman–Morrison formula In linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of a "rank-1 update" to a matrix whose inverse has previously been computed. That is, given an invertible matrix A and the ...

is a special case of the formula, with the term Sherman-Morrison-Woodbury sometimes used. An early overview of some of its uses has been given by Hager, see also the book "Woodbury Matrix Identity". These methods are taught in many mathematics courses on

Awards

* Fellow, 1960,

American Statistical Association The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts, on November 27, 1839, and is the second-oldest continuous ...

* Honored Fellow,

Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts ...

References

American mathematicians University of Utah alumni University of Michigan alumni University of North Carolina alumni University of Michigan faculty Princeton University faculty University of Pennsylvania faculty New York University faculty Duke University faculty Fellows of the American Statistical Association Fellows of the Institute of Mathematical Statistics 1917 births 2010 deaths {{US-mathematician-stub