45 research outputs found
More bounds for elgenvalues using traces
AbstractLet the n Ă n complex matrix A have complex eigenvalues λ1,λ2,âŠÎ»n. Upper and lower bounds for ÎŁ(Reλi)2 are obtained, extending similar bounds for ÎŁ|λi|2 obtained by Eberlein (1965), Henrici (1962), and Kress, de Vries, and Wegmann (1974). These bounds involve the traces of AâA, B2, C2, and D2, where B=12 (A + Aâ), C=12 (A â Aâ) /i, and D = AAâ â AâA, and strengthen some of the results in our earlier paper âBounds for eigenvalues using tracesâ 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 (1944â2005), this article
continues with personal comments by Oskar Maria Baksalary, Tadeusz CaliÂŽnski,
R.William Farebrother, JĂŒrgen GroĂ, Jan Hauke, Erkki Liski, Augustyn Markiewicz,
Friedrich Pukelsheim, Tarmo Pukkila, Simo Puntanen, Tomasz Szulc, Yongge Tian,
Götz Trenkler, JĂșlia VolaufovĂĄ, 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 CaliÂŽnski on Jerzy Baksalaryâs 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 paperâs 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