Estimates for the real and imaginary parts of the eigenvalues of matrices and applications

DOI10.1080/03081087.2016.1160997zbMath1361.15021OpenAlexW2302707740MaRDI QIDQ2953393

Omar Hirzallah, Ibrahim Halil Gümüş, Fuad Kittaneh

Publication date: 4 January 2017

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2016.1160997

zbMATH Keywords

zeros of a polynomialFrobenius normnormal matrixspread of a matrixreal and imaginary parts of an eigenvalue

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Real polynomials: location of zeros (26C10)

Related Items (4)

On spectra and real energy of complex weighted digraphs ⋮ On three classes of matrices with variants of the diagonal dominance property ⋮ Clarkson inequalities related to convex and concave functions ⋮ Norm inequalities involving convex and concave functions of operators

Cites Work

• Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials
• More estimates for eigenvalues and singular values
• Some lower bounds for the spectral radius of matrices using traces
• Eigenvalue estimates for symmetric matrices
• Improving bounds for eigenvalues of complex matrices using traces
• Bounds for eigenvalues using traces
• Bounds for singular values using traces
• Bounds for the zeros of polynomials from matrix inequalities
• New eigenvalue estimates for complex matrices
• Inequalities involving the mean and the standard deviation of nonnegative real numbers
• The spread of a matrix
• Bounds and a majorization for the real parts of the zeros of polynomials
• Matrix Analysis
• Operator norms as bounds for roots of algebraic equations

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