Remarks:

1. The papers that did not appear and will not be appearing soon are not listed here.

2. In all oy my papers, a pure imaginary number refers to a number of the form $bi$, where $b$ is any real number (including zero). Thus, in our definition of pure imaginary, we do not exclude the number zero. In other words, we consider 0 a pure imaginary number.

Here is the summary:

1. On Matrix $I^{(-1)}$ of Sind Methods. In this paper, we study properties of matrix $I^{(-1)}$ of sinc methods, which is defined as follows:
   Definition 0.1   $I^{(-1)}$ is the $n\times n$ matrix defined as follows:

   $$I^{(-1)}=\left[ \eta _{ij}\right] _{i,j=1}^{n}$$

   where $\eta _{ij}=e_{i-j}$, $$e_{k}=\frac{1}{2}+s_{k}$$, and $$s_{k}=\int _{0}^{k}\operatorname {sinc}(x)dx.$$

   Sinc methods are a family of formulas based on the sinc function which give accurate approximations of derivatives and definite and indefinite integrals and convolutions. These methods were developed by Frank Stenger. One of the nice properties of these methods is that they can handle boundary layer problems, integrals with infinite intervals or with singular integrands, and ODEs or PDEs that have coefficients with singularities.

   In this paper, we study properties of this Toeplitz matrix $I^{(-1)}$. This matrix and its properties are very important in the theory of Sinc indefinite integration and Sinc convolution

2. Rank-one Perturbations and Transformations of Centrosymmetric Matrices. In this paper, we study the effect of transformations and rank-one perturbations of centrosymmetric matrices on the eigenvalues, eigenvectors, determinants, and inverses.

3. Centrosymmetric Matrices: Properties and an Alternative Approach. In this paper, we describe a different approach of looking at and handling centrosymmetric matrices. This approach can be used as an alternative method to derive most of the known results about centrosymmetric matrices and new ones. We also identify orthogonal transformations between centrosymmetric matrices and skew-centrosymmetric matrices. One of these transformations is very helpful for reducing centrosymmetric (resp. skew-centrosymmetric) problems to skew-centrosymmetric (resp. centrosymmetric) problems. We also reveal properties for centrosymmetric matrices and skew-centrosymmetric matrices. In addition, we study a new charactarization of centrosymmetric matrices and skew-centrosymmetric matrices.

4. Centrosymmetric and Skew-centrosymmetric Matrices and Regular Magic Squares. In this paper, we reveal new properties of centrosymmetric and skew-centrosymmetric matrices. We also study properties of structured matrices involving these two types of matrices. For example, we study properties (determinants, eigen structure, singular values, etc) of structured complex matrices that invlove centrosymmetric and skew-centrosymmetric matrices. Hermitian persymmetric matrices are special cases of the matrices we study (which implies Goldstein reduction theorem for Herimitian persymmetric matrices follows as a corollary from our results). As another example, we study properties of regular magic squares and present another proof for the singularity of regular magic squares of even order. We also study singular values of centrosymmetric matrices and skew-centrosymmetric matrices, and mention some of their transformations. Although it is easy to see that the most known property that characterizes the eigen structure of centrosymmetric does not hold for skew-centrosymmetric matrices does not hold for skew-centrosymmetric matrices, we study a property for the special case when the matrix is real and skew-symmetric.

5. On the Counteridentity Matrix. In this paper, we make a comparison between the identity matrix and the counteridentity matrix (aka flip matrix, exchange matrix, contra identity, anti-identity). By the main counterdiagonal of a square matrix, we mean the positions which proceed diagonally from the last entry in the first row to the first entry in the last row. The main counterdiagonal is sometimes called the secondary diagonal or the main anti-diagonal. We will simply say counterdiagonal when we refer to the main counterdiagonal. The counteridentity matrix, denoted $J$, is the matrix whose elements are all equal to zero except those on the counterdiagonal, which are all equal to 1. Our paper reveals a structured matrix with the following property: if $a + bi$ is an eigenvalue of this matrix, then either $a = 0$ or $b = 0$, which means its eigenvalues can be either real or pure imaginary. It also describes the eigenvalues of matrices whose entries are all zeros except possibly those on the main diagonal or the main counterdiagonal. In other words, if $A=(a_{ij})$ is such a matrix ($A$ is $n\times n$), then $a_{ij} = 0$ if $j \neq i$ and $j \neq n-i+1$. We construct an analytic homotopy $H(t)$ in the space of diagonalizable matrices, between the counteridentity and any real skew-symmetric skew-centrosymmetric matrix such that $H(t)$ has only real or pure imaginary eigenvalues for $0\leq t\leq 1$. We study similartites and differences between the identity and the counteridentity.