Characteristic Roots and Field of Values of a Matrix
نویسنده
چکیده
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 values of the matrix [14]. In an address delivered before the Mathematical Association of America in 1938, Browne [10] gave a summary of these results up to that time. It is the purpose here to discuss some of the results obtained since the time of Browne's paper.
منابع مشابه
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