Then the determinantal varieties fall into the general study of degeneracy loci.

There, they develop quasideterminantal versions of many familiar determinantal properties.

These two formulae are known as "determinantal identities".

Most recently determinantal and permanental point processes (connected to random matrix theory) are beginning to play a role.

The following two conditions are necessary and sufficient for the existence of a determinantal random point process with intensities ρ.

In algebraic geometry, determinantal varieties are spaces of matrices with a given upper bound on their ranks.

In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press.

The ideal of k[x] generated by these polynomials is a determinantal ideal.

The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required.

An important class of point processes, with applications to physics, random matrix theory, and combinatorics, is that of determinantal point processes.

One can "globalize" the notion of determinantal varieties by considering the space of linear maps between two vector bundles on an algebraic variety.

This serves as an example of a well-defined determinantal point process with non-Hermitian kernel (although its restriction to the positive and negative semi-axis is Hermitian).

In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function.

The Segre variety is an example of a determinantal variety; it is the zero locus of the 2x2 minors of the matrix .

He is known for the famous determinantal identities, known as Frobenius-Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms.

Winfried Bruns, Udo Vetter, Determinantal rings, Lecture Notes in Mathematics, 1327.

Many more identities have appeared since the first articles of Gelfand and Retakh on the subject, most of them being analogs of classical determinantal identities.

To complete this discussion, we may observe that the companion matrix, or its equivalent - the regression formula, may be used to find complex roots of a determinantal equation (see 1.7.6).

Bálint Virág (born 1973) is a Hungarian mathematician working in Canada, known for his work in probability theory, particularly determinantal processes, random matrix theory, and random walks and other probabilistic questions on groups.

J. Ben Hough, Manjunath Krishnapur, Yuval Peres, and Bálint Virág (2009), Zeros of Gaussian Analytic Functions and Determinantal Processes, American Mathematical Society.

In mathematics, the determinantal conjecture of and asks whether the determinant of a sum X + Y of two n by n normal complex matrices X and Y lies in the convex hull of the n!

In mathematics, the Porteous formula, or Thom-Porteous formula, or Giambelli-Thom-Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes.