Abstract. A well–known property of an irreducible non–singular M–matrix is that its inverse is non–negative. However, when the matrix is an irreducible and singular M–matrix it is known that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. We focus here in characterizing when the Moore–Penrose inverse of a symmetric, singular, irreduci...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

BACKGROUND Renal calcium stones and hypercalciuria are associated with a reduced bone mineral density (BMD). Therefore, the effect of changes in calcium homeostasis is of interest for both stones and bones. We hypothesized that the response of calciuria, parathyroid hormone (PTH) and 1.25 vitamin D to changes in dietary calcium might be related to BMD. METHODS A single-centre prospective inte...

BACKGROUND Low serum 25-hydroxyvitamin D ¿25(OH)D concentrations are commonly found in the elderly and are associated with hip fracture. Treatment with vitamin D and calcium can reduce the risk of fracture. The relation between the rise in parathyroid hormone (PTH) with age and the decrease in 25(OH)D is not clear. Neither is there any consensus on the serum concentration of 25(OH)D required fo...

BACKGROUND Although the seasonal variance in serum levels of vitamin D in the elderly is well known, its significance on parathyroid hormone (PTH) remains controversial. OBJECTIVE To identify the variability and correlation between serum levels of vitamin D and PTH in a sample of community-dwelling elderly patients in the Province of Quebec, Canada, where vitamin D and calcium are supplemente...

Osteoporosis is an important contributor to the global burden of disease, and in the UK alone results in one in three women and one in twelve men aged >50 years experiencing a fragility fracture. Optimising peak bone mass in early adulthood is thought to reduce osteoporosis risk by offsetting bone losses in later life. Ensuring sufficient vitamin D status (measured as 25-hydroxyvitamin D (25OHD...