Wronskians and Linear Independence

被引：42

作者：

Bostan, Alin ^{[1
]}

Dumas, Philippe ^{[1
]}

机构：

[1] Inria Paris Rocquencourt, Algorithms Project, F-78153 Le Chesnay, France

来源：

关键词：

D O I：

10.4169/000298910X515785

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.

引用

页码：722 / 727

页数：6

共 24 条

[1] [Anonymous], 1944, Ordinary Differential Equations
[2] [Anonymous], 2006, An invitation to modern number theory
[3] [Anonymous], 1980, LECT NOTES MATH
[4] The theory of linear dependence.
Bocher, M
[J]. ANNALS OF MATHEMATICS, 1900, 2 (01) : 81 - 96
[5] Bocher M., 1900, B AM MATH SOC, V7, P120, DOI DOI 10.1090/50002-9904-1900-00771-3
[6] Certain cases in which the vanishing of the wronskian is a sufficient condition for linear dependence
Bocher, Maxime
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1901, 2 (1-4) : 139 - 149
[7] Cassels J.W.S., 1957, CAMBR TRACTS MATH MA, V45
[8] The vanishing of the Wronskian and the problem of linear dependence
Curtiss, DR
[J]. MATHEMATISCHE ANNALEN, 1908, 65 : 282 - 298
[9] THE APPROXIMATION TO ALGEBRAIC NUMBERS BY RATIONALS
DYSON, FJ
[J]. ACTA MATHEMATICA, 1947, 79 (04) : 225 - 240
[10] Frobenius G., 1874, J REINE ANGEW MATH, V77, P245