Displaying similar documents to “Is it wise to keep laminating ?”

Possible numbers ofx’s in an {x,y}-matrix with a given rank

Chao Ma (2017)

Open Mathematics

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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.

A bound for the rank-one transient of inhomogeneous matrix products in special case

Arthur Kennedy-Cochran-Patrick, Sergeĭ Sergeev, Štefan Berežný (2019)

Kybernetika

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We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.

Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.

A complete characterization of invariant jointly rank- convex quadratic forms and applications to composite materials

Vincenzo Nesi, Enrico Rogora (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank- convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank- convex forms arises. In the present paper, we define the concept of extremal -forms  and characterize them in the rotationally invariant...

On the Yang-Baxter-like matrix equation for rank-two matrices

Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)

Open Mathematics

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Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.

Latent Semantic Indexing using eigenvalue analysis for efficient information retrieval

Cherukuri Kumar, Suripeddi Srinivas (2006)

International Journal of Applied Mathematics and Computer Science

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Text retrieval using Latent Semantic Indexing (LSI) with truncated Singular Value Decomposition (SVD) has been intensively studied in recent years. However, the expensive complexity involved in computing truncated SVD constitutes a major drawback of the LSI method. In this paper, we demonstrate how matrix rank approximation can influence the effectiveness of information retrieval systems. Besides, we present an implementation of the LSI method based on an eigenvalue analysis for rank...