The representation given in Example 3 has an interesting property. The set of matrices {ρ(e), ρ(g)} have common invariant subspaces (other than the trivial ones, namely (0, 0) and C). Indeed, we can eas­ ily verify that the (orthogonal) one­dimensional subspaces given by (t, t) and (t, −t) are invariant under the action of these matrices. Therefore, the restriction of ρ to those subspaces also ...

In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

Invariant coordinate selection (ICS ) has recently been introduced by Tyler et al. (2008) as a method for exploring multivariate data. It includes as shown in Oja et al. (2006) as a special case a method for recovering the unmixing matrix in independent components analysis (ICA). It also serves as a basis for classes of multivariate nonparametric tests. The aim of this paper is to briefly expla...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...