Limits for the characteristic roots of a matrix. VII
نویسندگان
چکیده
منابع مشابه
Limits for the Characteristic Roots of a Matrix
Let A be a square matrix of order n with complex numbers as elements. The equation |XJ—A | = 0 is called the characteristic equation of the matrix A, and the roots X;, the characteristic roots of the matrix A. Although it is not possible to make any definite statements regarding the nature of the characteristic roots for the general matrix, several authors have given upper limits to the roots. ...
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If A is a square matrix of order n and I is the unit matrix, the equation in X obtained by equating to zero the determinant \A— \l\ is called the characteristic equation of A. The roots of this equation are called the characteristic roots of A. Although it is not possible to make any definite statement as to the nature of the characteristic roots of the general algebraic matrix A, several autho...
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From (1) it follows tha tX = x^4x*. The set of all complex numbers zAz* where zz* — \ is called the field of values [25] of the matrix A. It follows that the characteristic roots of A belong to the field of values of A. Beginning with Bendixson [3] in 1900, many writers have obtained limits for the characteristic roots of a matrix. In many cases these were actually limits for the field of value...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 1958
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-58-02552-3