Empirical studies comparing the effectiveness of visual languages versus textual languages have rarely been attempted. Here we describe an experiment conducted on programmers solving vector and matrix manipulation tasks using the visual language Forms/3, the textual language Pascal, and a textual matrix manipulation language with the capabilities of APL. Presented here are our motivation, exper...

Low-rank matrix recovery (LRMR) model, aiming at decomposing a matrix into a low-rank matrix and a sparse one, has shown the potential to address the problem of saliency detection, where the decomposed low-rank matrix naturally corresponds to the background, and the sparse one captures salient objects. This is under the assumption that the background is consistent and objects are obviously dist...

Every polynomial of degree n has n roots; every continuous function on [0, 1] attains its maximum; every real symmetric matrix has a complete set of orthonormal eigenvectors. “General theorems” are a big part of the mathematics we know. We can hardly resist the urge to generalize further! Remove hypotheses, make the theorem tighter and more difficult, include more functions, move into Hilbert s...

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them techniques. By leveraging properties of Pascal functionals and Wronskian matrices, derive several identities for these polynomials, including recurrence relations. It is highlighted that identities, acquired via techniques, are distinct from the ones obta...

In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subd...

We introduce a function on sequences, which we call the Pfaffian transform, using the Pfaffian of a skew-symmetric matrix. We establish several basic properties of the Pfaffian transform, and we use the transfer matrix method to show that the set of sequences with rational generating functions is closed under the Pfaffian transform. We conclude by computing the Pfaffian transform of a variety o...