Difference between revisions of "Functional determinant"
From Encyclopedia of Mathematics
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| − | A determinant whose elements are functions. Functional determinants of specific types play an important role in mathematical analysis. In the first place this refers to the [[Jacobian|Jacobian]] and the [[Wronskian|Wronskian]]. The concept of a Jacobian is used in an essential way when studying differentiable mappings between domains of Euclidean spaces | + | {{TEX|done}} |
| + | A determinant whose elements are functions. Functional determinants of specific types play an important role in mathematical analysis. In the first place this refers to the [[Jacobian|Jacobian]] and the [[Wronskian|Wronskian]]. The concept of a Jacobian is used in an essential way when studying differentiable mappings between domains of Euclidean spaces $\mathbf R^n$, $n\geq2$; when changing the variable in multiple integrals; when clarifying conditions for determining an implicit function by a system of equations or when a system of given functions is dependent; etc. The concept of the Wronskian is extensively applied in the theory of linear ordinary differential equations. | ||
Latest revision as of 16:04, 17 July 2014
A determinant whose elements are functions. Functional determinants of specific types play an important role in mathematical analysis. In the first place this refers to the Jacobian and the Wronskian. The concept of a Jacobian is used in an essential way when studying differentiable mappings between domains of Euclidean spaces $\mathbf R^n$, $n\geq2$; when changing the variable in multiple integrals; when clarifying conditions for determining an implicit function by a system of equations or when a system of given functions is dependent; etc. The concept of the Wronskian is extensively applied in the theory of linear ordinary differential equations.
How to Cite This Entry:
Functional determinant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Functional_determinant&oldid=12808
Functional determinant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Functional_determinant&oldid=12808
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article