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A Hankel matrix has entries constant on each anti-diagonal: with indices starting at zero, $H_{ij}=a_{i+j}$. For example,This differs from a Toeplitz matrix, whose entries are constant along diagonals. A square Hankel matrix is symmetric, although it need not be positive semidefinite.

An important example uses moments $a_k=\int x^{k}d\mu (x)$ of a positive measure on the real line, assuming the needed moments are finite. For a real coefficient vector $c$,so the moment Hankel matrix is positive semidefinite. Taking the point mass at $x=2$ gives $a_k=2^k$ and $H=(1,2,4{)}^T(1,2,4)$, of rank one. Thus the matrix pattern connects sequences, polynomials and moment problems.

Mark Krein was a mathematician whose research joined functional analysis, operator theory, harmonic analysis and mathematical physics. He worked on the moment problem, integral equations and the spectral theory of linear operators, building an influential research school despite severe institutional discrimination.^[ref] The Krein-Milman theorem, proved with David Milman, gives a geometric expression of this work: a nonempty compact convex set in a locally convex Hausdorff space is the closed convex hull of its extreme points. In finite dimensions, the corresponding picture is a convex polygon reconstructed from its vertices.

Mikhail Samuilovich Livsic, also known as Moshe Livšic, was a mathematician whose work connected complex analysis with operator theory. He studied with Mark Krein and developed research on Hermitian operators, the moment problem and extensions of operators, later building a research school at Ben-Gurion University.^[ref] A recurring idea in his work was to describe an operator by analytic data rather than only by its action on vectors. Such a viewpoint connects the geometry of an infinite-dimensional space with the behavior of analytic functions, and supplies tools for questions arising in quantum theory.

Identity and discipline: www.math.bgu.ac.il/people/members

Additional identity: mathshistory.st-andrews.ac.uk/Biographies/Livsic/