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Wronskian, the Glossary

In mathematics, the Wronskian of n differentiable functions is the determinant formed with the functions and their derivatives up to order.^[1]

30 relations: Abel's identity, Alternant matrix, American Mathematical Society, Analytic function, Annals of Mathematics, Complex number, Determinant, Differentiable function, Differential equation, Frobenius endomorphism, Interval (mathematics), Józef Maria Hoene-Wroński, Linear differential equation, Linear independence, Mathematics, Mathesis (journal), Matrix (mathematics), Maxime Bôcher, Moore matrix, Paul Mansion, Princeton University, Real number, Roth's theorem, Square matrix, Taylor & Francis, The American Mathematical Monthly, Transactions of the American Mathematical Society, Vandermonde matrix, Variation of parameters, Wiley (publisher).
Determinants

Abel's identity

In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation. Wronskian and Abel's identity are ordinary differential equations.

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Alternant matrix

In linear algebra, an alternant matrix is a matrix formed by applying a finite list of functions pointwise to a fixed column of inputs. Wronskian and alternant matrix are determinants.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

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Annals of Mathematics

The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.

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Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

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Determinant

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. Wronskian and determinant are determinants.

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Differentiable function

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

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Frobenius endomorphism

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class that includes finite fields.

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Interval (mathematics)

In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".

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Józef Maria Hoene-Wroński

Józef Maria Hoene-Wroński (Josef Hoëné-Wronski; 23 August 1776 – 9 August 1853) was a Polish messianist philosopher, mathematician, physicist, inventor, lawyer, occultist and economist.

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Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form a_0(x)y + a_1(x)y' + a_2(x)y \cdots + a_n(x)y^.

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Mathesis (journal)

Mathesis: Recueil Mathématique was a Belgian scientific journal for elementary mathematics, established in 1881 by Paul Mansion and Joseph Jean Baptiste Neuberg.

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Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

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Maxime Bôcher

Maxime Bôcher (August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra.

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Moore matrix

In linear algebra, a Moore matrix, introduced by, is a matrix defined over a finite field. Wronskian and Moore matrix are determinants.

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Paul Mansion

Paul Mansion (3 June 1844 – 16 April 1919) was a Belgian mathematician, editor of the journal Mathesis.

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Princeton University

Princeton University is a private Ivy League research university in Princeton, New Jersey.

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Roth's theorem

In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers.

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Square matrix

In mathematics, a square matrix is a matrix with the same number of rows and columns.

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Taylor & Francis

Taylor & Francis Group is an international company originating in England that publishes books and academic journals.

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The American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

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Vandermonde matrix

In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an (m + 1) \times (n + 1) matrix \begin 1 & x_0 & x_0^2 & \dots & x_0^n\\ 1 & x_1 & x_1^2 & \dots & x_1^n\\ 1 & x_2 & x_2^2 & \dots & x_2^n\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & x_m & x_m^2 & \dots & x_m^n \end with entries V_. Wronskian and Vandermonde matrix are determinants.

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Variation of parameters

In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. Wronskian and variation of parameters are ordinary differential equations.

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Wiley (publisher)

John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.

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References

[1] https://en.wikipedia.org/wiki/Wronskian

Also known as Generalized Wronskian, Wronski determinant, Wronskian determinant, Wrońskian.