Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers ψ :...

We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block diagonal with 1×1 and 2×2 blocks, or the identity with L lower triangular. We prove that with diagonal pivoting, th...

We present some observations on the block triangular form (btf) of structurally symmetric, square, sparse matrices. If the matrix is structurally rank deficient, its canonical btf has at least one underdetermined and one overdetermined block. We prove that these blocks are transposes of each other. We further prove that the square block of the canonical btf, if present, has a special fine struc...

In this paper, the UDUT decomposition of the generalized inertia matrix o f an n-link serial manipulator is presented in symbolic form, where U and D, respectively, are the upper triangular and diagonal matrices. To render the decomposition, the elementary upper triangular matrices, associated to a modified Gaussian elimination, are introduced, whereas each element of the inertia matrix is writ...

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...