For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed inverse spectral problem is studied, and the description of the space of its solutions is given. We apply the developed technique to give sufficient conditions for...

Complex orthogonal designs (CODs) are used to construct space-time block codes. COD Oz with parameter [p, n, k] is a p × n matrix, where nonzero entries are filled by ±zi or ±z ∗ i , i = 1, 2, . . . , k, such that O H z Oz = (|z1| 2 + |z2| 2 + . . . + |zk| )In×n. Define Oz a first type COD if and only if Oz does not contain submatrix (

We present a real symmetric tridiagonalmatrix of order nwhose eigenvalues are {2k}n−1 k=0 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l + 1}n−2 l=0 . Thematrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution ...

Every stable controllable input pair (Ã , B̃ ) is equivalent to an input pair which is in Hessenberg form and is input normal (AA∗ + BB∗ = I ). (A,B) is represented as a submatrix of the minimal number of Givens rotations. The representation is shown to be generically identifiable. This canonical form allows for fast state vector updates and improved conditioning of system identification problem...

Biclustering (also known as submatrix localization) is a problem of high practical relevance in exploratory analysis of high-dimensional data. We develop a framework for performing statistical inference on biclusters found by score-based algorithms. Since the bicluster was selected in a data dependent manner by a biclustering or localization algorithm, this is a form of selective inference. Our...

A zero-one matrix A contains another zero-one matrix P if some submatrix of A can be transformed to P by changing some ones to zeros. A avoids P if A does not contain P. The Pattern Avoidance Game is played by two players. Starting with an all-zero matrix, two players take turns changing zeros to ones while keeping A avoiding P. We study the strategies of this game for some patterns P. We also ...

We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if Lie sub(super)algebra determined by it not finite dimensional or but (super)algebra any submatrix A, obtained striking out row and column intersecting on main diagonal, sum (super)algebras. said to be affine, all its matrices are affine. list superalgebras over complex numbers ...

A 0,±1 matrix is balanced if it does not contain a square submatrix with two nonzero elements per row and column in which the sum of all entries is 2 modulo 4. Conforti, Cornuéjols and Rao [9], and Conforti, Cornuéjols, Kapoor and Vušković [6], provided a polynomial algorithm to test balancedness of a matrix. In this paper we present a simpler polynomial algorithm, based on techniques introduce...