Bibliography

1

O. Axelsson, H. Lu, and B. Polman, On the numerical radius of matrices and its application to iterative solution methods, Linear and Multilinear Algebra, 37 (1994), pp. 225-238.

2

C.A. Berger, On the numerical range of powers of an operator, Notices of the American Mathematical Society, 12 (1965), p. 590.

3

F.F. Bonsall and Duncan, Numerical Ranges I, Cambridge University Press, Cambridge, 1971.

4

F.F. Bonsall and Duncan, Numerical Ranges II, Cambridge University Press, Cambridge, 1973.

5

S.-H. Cheng and N.J. Higham, The nearest definite pair for the Hermitian generalized eigenvalue problem, Linear Algebra and Its Applications, 302-303 (1999), pp. 63-76.

6

C. Davis, The Toeplitz-Hausdorff Theorem explained, Canadian Mathematical Bulletin, 14 (1971), pp. 245-246.

7

W. Donoghue, On the numerical range of a bounded operator, Michigan Math. J., 4 (1957), pp. 261-263.

8

M. Eiermann, Field of values and iterative methods, Linear Algebra and Its Applications, 180 (1993), pp. 167-197.

9

M. Fiedler, Geometry of the numerical range of matrices, Linear Algebra and Its Applications, 37 (1981), pp. 81-96.

10

M. Fiedler, Numerical range of matrices and Levinger's theorem, Linear Algebra and Its Applications, 220 (1995), pp. 171-180.

11

W. Givens, Field of values of a matrix, Proceedings of American Mathematical Society, 3 (1952), pp. 206-209.

12

M. Goldberg and E. Tadmor, On the numerical radius and its applications, Linear Algebra and Its Applications, 42 (1982), pp. 263-284.

13

K.E. Gustafson and D.K.M. Rao, Numerical Range, Springer, New York, 1997.

14

P.R. Halmos, A Hilbert Space Problem Book, Von Nostrand, New York, 1967.

15

F. Hausdorff, Der Wertvorrat einer Bilinearform, Math. Z., 3 (1919), pp. 314-316.

16

R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.

17

J. N. Issos. The field of values of non-negative irreducible matrices. Ph.D. Thesis, Auburn University, 1966.

18

C.R. Johnson, Numerical determination of the field of values of a complex matrix, SIAM J. Num. Analysis, 15 (1978), pp. 595-602.

19

R. Kippenhahn, Über den wertevorrat einer matrix, Math. Nachr., 6 (1951), pp. 193-228.

20

S. Kirkland, P. Psarrakos, and M. Tsatsomeros, On the location of the spectrum of hypertournament matrices, Linear Algebra and Its Applications, 323 (2001), pp. 37-49.

21

H. Langer, A. Markus, and C. Tretter, Corners of numerical ranges, Operator Theory: Advances and Applications, 124 (2001), pp. 383-400.

22

C.-K. Li, $C$-numerical ranges and $C$-numerical radii, Linear and Multilinear Algebra, 37 (1994), pp. 51-82.

23

Y. Lyubich and A. Markus, Connectivity of level sets of quadratic forms and Hausdorff-Toeplitz type theorems, Positivity, 1 (1997), pp. 239-254.

24

J. Maroulas, P. Psarrakos, and M. Tsatsomeros, Perron-Frobenius type results on the numerical range, Linear Algebra and Its Applications, 348 (2002), pp. 49-62.

25

F.D. Murnaghan, On the field of values of a complex matrix, Proc. Nat. Acad. Sci. USA, 18 (1932), pp. 246-248.

26

C. Pearcy, An elementary proof of the power inequality for the numerical radius, Michigan Math. J., 13 (1960), pp. 289-291.

27

P. Psarrakos and M. Tsatsomeros, On the stability radius of matrix polynomials, Linear and Multilinear Algebra, 50 (2002), pp. 151-165.

28

H. Shapiro, A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices II, Linear Algebra and Its Applications, 45 (1982), pp. 97-108.

29

M. Stone, Linear Transformations in Hilbert Space, American Mathematical Society, Providence, 1932.

30

B.-S. Tam and S. Yang, On matrices whose numerical ranges have circular or weak circular symmetry, Linear Algebra and Its Applications, 302/303 (1999), pp. 193-221.

31

O. Toeplitz, Das algebraische Analogon zu einern Satze von Fejér, Math. Z., 2 (1918), pp. 187-197.

32

P.-Y. Wu, A numerical range characterization of Jordan blocks, Linear and Multilinear Algebra, 43 (1998), pp. 351-361.