In mathematics,particularly linear algebra and functional analysis,a spectral theorem is a result about when a linear operator or matrix can be diagonalized. This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general,the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators,which are as simple as one can hope to find. In more abstract language,the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical perspective.
In mathematics,spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial,eigenvalues,and eigenvectors of matrices associated with the graph,such as its adjacency matrix or Laplacian matrix.
In functional analysis,compact operators are linear operators on Banach spaces that map bounded sets to relatively compact sets. In the case of a Hilbert space H,the compact operators are the closure of the finite rank operators in the uniform operator topology. In general,operators on infinite-dimensional spaces feature properties that do not appear in the finite-dimensional case,i.e. for matrices. The compact operators are notable in that they share as much similarity with matrices as one can expect from a general operator. In particular,the spectral properties of compact operators resemble those of square matrices.
Barbara Diane MacCluer is an American mathematician,formerly a professor of mathematics at the University of Virginia and now a professor emeritus there. Her research specialty is in operator theory and composition operators;she is known for the books she has written on this subject and related areas of functional analysis.
Jean Estelle Hirsh Rubin was an American mathematician known for her research on the axiom of choice. She worked for many years as a professor of mathematics at Purdue University. Rubin wrote five books:three on the axiom of choice,and two more on more general topics in set theory and mathematical logic.
Ping Zhang is a mathematician specializing in graph theory. She is a professor of mathematics at Western Michigan University and the author of multiple textbooks on graph theory and mathematical proof.
Tatjana (Tanja) Eisner is a German and Ukrainian mathematician specializing in functional analysis,operator theory as well as ergodic theory and its connection to number theory. She is a professor of mathematics at Leipzig University.
Hazel Perfect was a British mathematician specialising in combinatorics.
Hilary Ockendon is a British mathematician who worked at the University of Oxford until retirement in 2008. Her research focuses on applications of mathematics with a particular interest in continuum models for industrial problems. She is an emeritus fellow of Somerville College,Oxford,the former president of the European Consortium for Mathematics in Industry,and the author of multiple books on fluid dynamics. She is an expert on problems in fluid dynamics,such as the reduction of sloshing in coffee cups.
Elizabeth Samantha Meckes (1980–2020) was an American mathematician specializing in probability theory. Her research included work on Stein's method for bounding the distance between probability distributions and on random matrices. She was a professor of mathematics,applied mathematics,and statistics at Case Western Reserve University. She died in December 2020 after a brief battle with cancer.
Anne C. Morel was an American mathematician known for her work in logic,order theory,and algebra. She was the first female full professor of mathematics at the University of Washington.
Giuliana P. Davidoff is an American mathematician specializing in number theory and expander graphs. She is the Robert L. Rooke Professor of Mathematics and the chair of mathematics and statistics at Mount Holyoke College.
Clàudia Valls Anglés is a mathematician and an expert in dynamical systems. She is an associate professor in the Instituto Superior Técnico of the University of Lisbon in Portugal.
Yuliya Stepanivna Mishura is a Ukrainian mathematician specializing in probability theory and mathematical finance. She is a professor at the Taras Shevchenko National University of Kyiv.
Margaret Alice Waugh Maxfield was an American mathematician and mathematics book author.
Thomas Shelburne Ferguson is an American mathematician and statistician. He is a professor emeritus of mathematics and statistics at the University of California,Los Angeles.
Jane Grace Kehoe Cullum is an American applied mathematician known for her work in numerical algorithms and control theory,who became president of the IEEE Control Systems Society.
Laura Toti Rigatelli (1941-2023) was an Italian historian of mathematics,founder of the Center for Medieval Mathematics at the University of Siena,biographer of Évariste Galois,and author of many books on the history of mathematics.
Ulrike Leopold-Wildburger is an Austrian mathematical economist,applied mathematician,and operations researcher. She is a professor emeritus at the University of Graz,where she headed the department of statistics and operations research,and is a former president of the Austrian Society of Operations Research.
Meike Maria Elisabeth Akveld is a Swiss mathematician and textbook author,whose professional interests include knot theory,symplectic geometry,and mathematics education. She is a tenured senior scientist and lecturer in the mathematics and teacher education group in the Department of Mathematics at ETH Zurich. She is also the organizer of the Mathematical Kangaroo competitions in Switzerland,and president of the Association Kangourou sans Frontières,a French-based international society devoted to the popularization of mathematics.
