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An square matrix is $k$-Toeplitz if its diagonals are periodic sequences of period $k$. We find rational formulas for the determinant, the characteristic polynomial, and the elements of the inverse of a tridiagonal $k$-Toeplitz matrix (in particular, of any tridiagonal matrix) over any commutative unital ring, using only elementary linear algebra.
Let $R$ be the associative $k$-algebra generated by two elements $x$ and $y$ with defining relation $yx=1$. A complete description of simple modules over $R$ is obtained by using the results of Irving and Gerritzen. We examine the short exact sequenc
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain insight. Fe
Let A denote the ring of differential operators on the affine line with its two usual generators t and d/dt given degrees +1 and -1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups Z/2 at each
Let $Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring $Q=Bbbk[x_1,ldots,x_n]$. In her thesis, Taylor introduced a complex which provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda constructed a differenti
Recently, by A. Elduque and A. Labra a new technique and a type of an evolution algebra are introduced. Several nilpotent evolution algebras defined in terms of bilinear forms and symmetric endomorphisms are constructed. The technique then used for t