In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order...

Hesse and later named after him. Hesse originally used the term "functional determinants". The Hessian is sometimes denoted by H or ∇ ∇ {\displaystyle \nabla...

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A)...

mathematical functions Clifford algebra Tensor field Spectral theory Functional determinant Fulton, William; Harris, Joe (1991). Representation Theory: A First...

square of the imaginary part of the Riemann zeros, and also that the functional determinant of this Hamiltonian operator is just the Riemann Xi function. In...

divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators. The technique is now commonly...

is that π can be obtained from the functional determinant of the harmonic oscillator. This functional determinant can be computed via a product expansion...

relational model of data, a natural key is a superkey and is therefore a functional determinant for all attributes in a relation. A natural key serves two complementary...

classifying patients in class II or III, because functional capacity is such a powerful determinant of outcome, it remains arguably the most important...

In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection.: 38  Due to a lack of harmonization...

In functional analysis, the Hilbert–Carleman determinant is an operator determinant for certain integral operators on Banach spaces, whose kernels are...

wavefunction can be represented as a Slater determinant of orbitals. Further, the kinetic energy functional of such a system is known exactly. The exchange–correlation...

symmetric matrices are real. Jacobi studied "functional determinants"—later called Jacobi determinants by Sylvester—which can be used to describe geometric...

is also treated in these papers. In 1773, Lagrange considered a functional determinant of order 3, a special case of a Jacobian. He also proved the expression...

Polyakov formula expresses the conformal variation of the zeta functional determinant of a Riemannian manifold. Proposed by Alexander Markovich Polyakov...

) ∞ {\displaystyle (2\pi )^{\infty }} is infinite and also, the functional determinant would also be infinite in general. This can be taken care of if...

anomaly in quantum field theory. It uses the correspondence between functional determinants and the partition function, effectively making use of the Atiyah–Singer...

_{i}^{-s}} . It is used in giving a rigorous definition to the functional determinant of an operator, which is given by det O := e − ζ O ′ ( 0 ) . {\displaystyle...

perturbation takes place. The ghost term in the Lagrangian represents the functional determinant of the Jacobian of this embedding, and the properties of the ghost...

An epitope, also known as antigenic determinant, is the part of an antigen that is recognized by the immune system, specifically by antibodies, B cells...

)}(\eta (A))\det(\mathrm {d} \eta /\mathrm {d} A)\mathrm {d} A} . The functional determinant and associated mathematical subtleties drop out if the Langevin...

of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a...

to evolutionary ideas of the Enlightenment. Lagrange considers a functional determinant of order 3, a special case of a Jacobian. He also proves the expression...

fermions (non-fermion Density Functional Theory has been researched), the Kohn–Sham wavefunction is a single Slater determinant constructed from a set of...

Quillen metric Quillen, Daniel (1985), "Determinants of Cauchy-Riemann operators over a Riemann surface", Functional Analysis and Its Applications, 19, Springer...

Relation between determinant and trace via eigenvalues). The number Δ ( X ) {\displaystyle \Delta (X)} is well-defined by continuous functional calculus. Δ...

to a basis are similar. The trace is related to the derivative of the determinant (see Jacobi's formula). The trace of an n × n square matrix A is defined...

Fujikawa derived this anomaly using the correspondence between functional determinants and the partition function using the Atiyah–Singer index theorem...

(entries not on the main diagonal are zero) whose diagonal entries are the determinant of the original matrix: A adj ⁡ ( A ) = det ( A ) I , {\displaystyle...

(x)\delta \phi (y)}}[B]\right)^{-1/2}+\cdots } where "det" signifies a functional determinant and C is a constant. The power of minus one half will naturally...