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Linear Algebra and its Applications, Vol. 29 (February 1980), pp. 471-506, doi:10.1016/0024-3795(80)90258-x Key: citeulike:11335493
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Several new inequalities are obtained for the modulus, the real part, and the imaginary part of a linear combination of the ordered eigenvalues of a square complex matrix. Included are bounds for the condition number, the spread, and the spectral radius. These inequalities involve the trace of a matrix and the trace of its square. Necessary and sufficient conditions for equality are given for each inequality.
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