Abstract:

Some characteristics about the real and imaginary part of matrix eigenvalues are discussed, and obtains some sharper upper bounds of the spread of a matrix. All the eigenvalues of an arbitrarily given matrix are located in elliptic regions is proved and give another upper bounds of the spread of a matrix. An example illustrates the effectiveness of our results.

Key words: eigenvalue; the spread of a matrix; Euclidean norm; elliptic region