Results 261 to 270 of about 294,893 (309)

Positive Powers of Positive Positive Definite Matrices

Canadian Journal of Mathematics, 1996
AbstractLet C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.
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Positive Definite Matrices, Characteristic Roots, and Positive Matrices

1965
As soon as we leave the well-traversed fields of real and complex numbers for the broader and relatively unexplored domains of hyper-complex numbers, we open the way for the introduction of many different types of ordering relationships. In this chapter, we shall discuss a variety of interesting inequalities centering about the theme of matrices. As we
Edwin F. Beckenbach, Richard Bellman
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Symmetric Decomposition of Positive Definite Band Matrices

Numerische Mathematik, 1965
The method is based on the following theorem. If A is a positive definite matrix of band form such that $${a_{ij}} = 0{\rm{ (|}}i - j| >m{\rm{)}}$$ (1) then there exists a real non-singular lower triangular matrix L such that $$L{L^T} = A,{\rm{ where }}{l_{ij}} = 0{\rm{ (}}i - j >m{\rm{)}}{\rm{.}}$$ (2)
Martin, R. S., Wilkinson, J. H.
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Positive Definite Block Matrices

1990
This chapter is a positive matrix version of Chapter IV. First we give a complete characterization of all 2 by 2 and 3 by 3 positive block matrices. Then this is used to obtain some standard results for positive Toeplitz matrices and the Levinson algorithm.
Ciprian Foias, Arthur E. Frazho
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Diagonalizing Positive Definite Matrices

Mathematics Magazine, 1966
(1966). Diagonalizing Positive Definite Matrices. Mathematics Magazine: Vol. 39, No. 4, pp. 226-227.
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Near order and metric-like functions on the cone of positive definite matrices

Positivity (Dordrecht), 2023
R. Dumitru, Jose A. Franco
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Tensor Dictionary Learning for Positive Definite Matrices

IEEE Transactions on Image Processing, 2015
Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding ...
Ravishankar, Sivalingam, Daniel, Boley, Vassilios, Morellas, Nikolaos, Papanikolopoulos   +3 more
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Conservative perturbations of positive definite Hamiltonian matrices

Numerical Linear Algebra with Applications, 2004
AbstractWe consider Hamiltonian matrices obtained by means of symmetric and positive definite matrices and analyse some perturbations that maintain the eigenvalues on the imaginary axis of the complex plane. To obtain this result we prove for such matrices the existence of a diagonal form or, alternatively by means of symplectic transformations, the ...
AMODIO, Pierluigi, IAVERNARO, Felice, TRIGIANTE D.   +2 more
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Maximum Submatrix Traces for Positive Definite Matrices

SIAM Journal on Matrix Analysis and Applications, 1993
The authors consider three \(p\)-dimensional jointly distributed random vectors \(X,Y\) and \(Z\) with respective normal marginal distributions \(N(0,\Sigma_{ii})\), \(i=1,2,3\) and determine certain covariance matrices that minimize the sum of the \(L_ 2\)-distances of the three vectors.
Olkin, I., Rachev, S. T.
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On symplectic eigenvalues of positive definite matrices

, 2015
If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(A)) is a diagonal matrix with positive diagonal entries, which are called the symplectic eigenvalues of A.
R. Bhatia, Tanvi Jain
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