A new algebra of Toeplitz-plus-Hankel matrices and applications ?
We introduce a new simultaneously diagonalizable real algebra A A of symmetrical centrosymmetrical matrices having a Toeplitz-plus-Hankel structure. We give the corresponding orthonormal basis of eigenvectors which are alternately symmetrical and skewsymmetrical vectors. An application is the construction of a symmetrical Toeplitz-plus-centrosymmetrical Hankel matrix of equal row sums having a prescribed real spectrum. This matrix can be used as the starting matrix for symmetrical centrosymmetrical isospectral flows. In particular, for the isospectral flow corresponding to the construction of a regular Toeplitz matrix having prescribed eigenvalues. Moreover, if A A is a noise representation of an unknown matrix in A A of rank k k then we give a procedure to approximate A A by a matrix in A A of rank k k .
centrosymmetrical matrices hankel matrix isospectral flow toeplitz matrix circulant matrices low rank approximation