Appendix B: Vector storage of arrays

The relation between the one-dimensional vectors (here symbolized by ${\vec{v}}$) and the matrices (M) they represent is as follows (i represents the rows, j the columns):

$$v(k) = M(i,j)~~{\rm for~all}~j\geq i~{\rm and}~k = j(j-1)/2 + i$$ (B1)

In a symmetric matrix the additional condition

M(j,i)=M(i,j)

applies, and in a lower triangular matrix:

$$M(i,j) = 0~~{\rm for~all}~j<i.$$ (B3)