منابع مشابه
The Characteristic Roots of a Matrix*
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...
متن کاملLimits 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. ...
متن کاملCharacteristic Roots and Field of Values of a Matrix
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...
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1930
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1930-05041-7