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Displaying 1621 – 1640 of 2599

On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix

Yusaku Yamamoto (2017)

Applications of Mathematics

Lower bounds on the smallest eigenvalue of a symmetric positive definite matrix $A \in ℝ^{m \times m}$ play an important role in condition number estimation and in iterative methods for singular value computation. In particular, the bounds based on $Tr (A^{- 1})$ and $Tr (A^{- 2})$ have attracted attention recently, because they can be computed in $O (m)$ operations when $A$ is tridiagonal. In this paper, we focus on these bounds and investigate their properties in detail. First, we consider the problem of finding the optimal bound that can be computed...

On the orbit of the centralizer of a matrix

Ching-I Hsin (2002)

Colloquium Mathematicae

Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.

On the order of linear dependence of real functions

Barbara Kraśnicka, Marian Malec (1974)

Colloquium Mathematicae

On the ordered sets in $n$ -dimensional real inner product spaces.

Demirel, Oğuzhan, Soytürk, Emine (2008)

APPS. Applied Sciences

On the parametric solution to the second-order Sylvester matrix equation $E V F^{2} - A V F - C V = B W$ .

Wang, Guo-Sheng, Lv, Qiang, Duan, Guang-Ren (2007)

Mathematical Problems in Engineering

On the partial ordering of almost definite matrices

Ar. Meenakshi (1989)

Czechoslovak Mathematical Journal

On the partitioned matrix $(\begin{matrix} O & A \\ A^{} & Q \end{matrix})$ and its associated system $A X = T, A^{} Y + Q X = Z$

Vladimiro Valerio (1981)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On the periodic quotient singular value decomposition.

Hench, J.J. (1994)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

On the permanents of certain circulant matrices and related Toeplitz matrices. (Über die Permanente gewisser zirkulanter Matrizen und damit zusammenhängender Toeplitz-Matrizen.)

Kräuter, Arnold Richard (1984)

Séminaire Lotharingien de Combinatoire [electronic only]

On the polynomial numerical hull of a normal matrix.

Afshin, Hamid Reza, Mehrjoofard, Mohammad Ali (2011)

Banach Journal of Mathematical Analysis [electronic only]

On the Prime Ideal of an Ordering of Higher Level.

Thomas C. Craven (1982)

Mathematische Zeitschrift

On the principal minors of a matrix with a multiple eigenvalue.

Ikramov, Kh.D. (2005)

Zapiski Nauchnykh Seminarov POMI

On the problem $A x = λ B x$ in max algebra: every system of intervals is a spectrum

Sergeĭ Sergeev (2011)

Kybernetika

We consider the two-sided eigenproblem $A \otimes x = λ \otimes B \otimes x$ over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.

On the pseudoinverse of a sum of symmetric matrices with applications to estimation

Pavel Kovanic (1979)

Kybernetika

On the reduction of a Hamiltonian matrix to Hamiltonian Schur form.

Watkins, David S. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

On the reduction of a random basis

Ali Akhavi, Jean-François Marckert, Alain Rouault (2009)

ESAIM: Probability and Statistics

For p ≤ n, let b1(n),...,bp(n) be independent random vectors in $ℝ^{n}$ with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If ${\hat{b}}_{1}^{(n)}, ..., {\hat{b}}_{p}^{(n)}$ is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...

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