Equations fonctionnelles et estimations de normes de matrices.
Generalized Schur complements of matrices and compound matrices.
Generalized -Newton inequalities revisited.
Gers̆gorin-type eigenvalue inclusion theorems and their sharpness.
Girth and subdominant eigenvalues for stochastic matrices.
Inclusion Domains for the Eigenvalues of Stochastic Matrices.
Inequalities for spreads of matrix sums and products.
Inequalities for the minimum eigenvalue of -matrices.
Inequalities for the trace function.
Inequalities on the singular values of an off-diagonal block of a Hermitian matrix.
Interlacing for weighted graphs using the normalized Laplacian.
Iterations of concave maps, the Perron-Frobenius theory, and applications to circle packings.
Jacobi matrices with prescribed eigenvalues and diagonal elements
Latent roots of lambda-matrices, Kronecker sums and matricial norms
Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for where is a latent root of a lambda-matrix. In particular, upper bounds for are obtained where is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for .
Loewner matrix ordering in estimation of the smallest singular value.
Log-majorizations and norm inequalities for exponential operators
Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.
Lower Bounds for the Condition Number of Vandermonde Matrices.
Lower bounds for the largest eigenvalue of the gcd matrix on
Consider the matrix with ’th entry . Its largest eigenvalue and sum of entries satisfy . Because cannot be expressed algebraically as a function of , we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S. Hong, R. Loewy (2004). We also conjecture that for all . If is large enough, this follows from F. Balatoni (1969).
Majorants of matrix norms and spectrum localization
Majorization bounds for Ritz values of Hermitian matrices.