The matrix pencil algebraic characterisation of the families of invariant subspaces of an implicit system S(F, G) : Fz = Gz F, G € K m x n , is further developed by using tools from Exterior Algebra and in particular the Grassmann Representative g(V) of the subspace V of the domain of (F,G). Two different approaches are considered: The first is based on the compound of the pencil C'd(sF — G), w...

Two algorithms are proposed for estimating the quadratically coupled frequency pairs (QC pairs) in a signal consisting of complex sinusoids in white noise, which may be nongaussian in general. Three matrices are constructed from the complex third order moments of the noisy signal, the latter two being time shifted versions of the first. The list of coupled frequencies is obtained from the rank ...

Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent to appending rows to this pencil to place new generalized eigenvalues. Adding inputs is likewise equivalent to appending columns. Since both problems are dual to each other, we only show in this pa...

It is cheap to process epidemiological data from optical mark read (OMR) questionnaires. Respondents should use a pencil to complete OMR questionnaires, but many will not unless these are supplied. Sending pencils and erasers is expensive. Does sending pencils and erasers increase the response rate as cost-effectively as sending reminders, or does this decrease the error rate and offset data ch...

In underwater sonar systems, identifying targets from their signatures is an important, but, yet, open problem. In an earlier document, we had proposed to extract the fundamental modes of a target based on the Matrix Pencil and Cauchy approaches. This report presents the results of a preliminary analysis of PONDEX data sets provided by Defense Research and Development Canada (DRDC) Atlantic. Th...