We take advantage of a recent development in Social Choice in order to propose a new algorithm for the prioritization of objects characterized by fuzzy soft sets. It benefits from the performance of an endogenous scoring rule recently proposed by Herrero [1]. Our procedure constructs a “comparison matrix” and grades the objects according to the corresponding component of an eigenvector associat...

Let A be an n × n real matrix. An eigenvector of A is a vector such that Ax is parallel to x; in other words, Ax = λx for some real or complex number λ. This number λ is called the eigenvalue of A belonging to eigenvector v. Clearly λ is an eigenvalue iff the matrix A − λI is singular, equivalently, iff det(A − λI) = 0. This is an algebraic equation of degree n for λ, and hence has n roots (wit...

In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows ...

1 Preliminaries • p. 28 l. -2 : Insert ‘provided the automaton is complete’ after ‘The matrix M/k is stochastic’. • p. 30 l. Replace lines 3–17 by : Applying by induction the theorem to U and W , we obtain nonnegative eigenvectors u and w for the eigenvalues ρU and ρW of U and W . We prove that max(ρU , ρW ) is an eigenvalue of M with some nonnegative eigenvector. If ρU ≥ ρW , then ρU is an eig...

An approach to schedule development in project management is developed within the framework of idempotent algebra. The approach offers a way to represent precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempotent algebra setting, inc...

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues....

Analysis of systems that can be expressed in matrices is very important the field application. Whether such a system works properly determined by eigenvalues matrix representing system. Eigenvalue and eigenvector concepts are taught within scope linear algebra course at undergraduate level. In this study, perceptions students who took about eigenvalue-eigenvector investigated. The research cond...

1 Preliminaries • p. 28 l. -2 : Insert ‘provided the automaton is complete’ after ‘The matrix M/k is stochastic’. • p. 30 l. Replace lines 3–17 by : Applying by induction the theorem to U and W , we obtain nonnegative eigenvectors u and w for the eigenvalues ρU and ρW of U and W . We prove that max(ρU , ρW ) is an eigenvalue of M with some nonnegative eigenvector. If ρU ≥ ρW , then ρU is an eig...