The Solution to a Structured Matrix Approximation Problem Using Grassman Coordinates

Authors:
Craig S. MacInnes
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1999

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Abstract

A method for finding the best approximation of a matrix A by a full rank Hankel matrix is given. The initial problem of best approximation of one matrix by another is transformed to a problem involving best approximation of a given vector by a second vector whose elements are constrained so that its inverse image is a Hankel matrix. The map from a matrix to a vector is the invertible map between a subspace represented as the row space of the matrix A and the Grassman vector representing that subspace. The relation between the principle angles associated with a pair of subspaces and the angle between the Grassman vectors associated with the subspaces is established.