“Characteristic Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Characteristic Equation

释义

Characteristic Equation

The equation which is solved to find a Matrix's Eigenvalues, also called theCharacteristic Polynomial. Given a system of equations with Matrix

(1)

the Matrix Equation is

(2)

which can be rewritten

(3)

M can have no Matrix Inverse, since otherwise

(4)

which contradicts our ability to pick arbitrary

and

. Therefore, M has no inverse, so its Determinantis 0. This gives the characteristic equation

(5)

where

denotes the Determinant of A. For a general

Matrix

(6)

the characteristic equation is

(7)

See also Ballieu's Theorem, Cayley-Hamilton Theorem, Parodi's Theorem, Routh-Hurwitz Theorem

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, pp. 1117-1119, 1979.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。