Foreword

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More bounds for elgenvalues using traces

AbstractLet the n × n complex matrix A have complex eigenvalues λ1,λ2,…λn. Upper and lower bounds for Σ(Reλi)2 are obtained, extending similar bounds for Σ|λi|2 obtained by Eberlein (1965), Henrici (1962), and Kress, de Vries, and Wegmann (1974). These bounds involve the traces of A∗A, B2, C2, and D2, where B=12 (A + A∗), C=12 (A − A∗) /i, and D = AA∗ − A∗A, and strengthen some of the results in our earlier paper “Bounds for eigenvalues using traces” in Linear Algebra and Appl. [12]

The efficiency factorization multiplier for the Watson efficiency in partitioned linear models: some examples and a literature review

We consider partitioned linear models where the model matrix X = (X1 : X2) has full column rank, and concentrate on the special case whereX0 1X2 = 0 when we say that the model is orthogonally partitioned. We assume that the underlying covariance matrix is positive definite and introduce the efficiency factorization multiplier which relates the total Watson efficiency of ordinary least squares to the product of the two subset Watson efficiencies. We illustrate our findings with several examples and present a literature review

Some comments on the life and work of Jerzy K. Baksalary (1944-2005)

Following some biographical comments on Jerzy K. Baksalary (1944–2005), this article continues with personal comments by Oskar Maria Baksalary, Tadeusz Cali´nski, R.William Farebrother, Jürgen Groß, Jan Hauke, Erkki Liski, Augustyn Markiewicz, Friedrich Pukelsheim, Tarmo Pukkila, Simo Puntanen, Tomasz Szulc, Yongge Tian, Götz Trenkler, Júlia Volaufová, Haruo Yanai, and Fuzhen Zhang, on the life and work of Jerzy K. Baksalary, and with a detailed list of his publications. Our article ends with a survey by Tadeusz Cali´nski on Jerzy Baksalary’s work in block designs and a set of photographs of Jerzy Baksalary

Superstochastic matrices and magic Markov chains

AbstractA brief account of the conceptual formulation of the two entities in this paper’s title, plus an initial preliminary investigation of some of their mathematical properties, is given

Bounds for eigenvalues using traces

AbstractSeveral 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