A symmetric, positive definite and
sparse, n by n matrix
•
a11   a12    0     0     0     0    0
a21   a22   a23   a24   0     0    0
  0     a32   a33    a34     0        0    0
  0     a42   a43   a44   a45    a46     0
  0       0       0      a54   a55    a56     0
 0        0      0       a46   a65    a66   a67
 0      0       0      0     0      a76  a77
A*= A
x* Ax > 0 for x ≠ 0
1.3
The matrices which we were confronted with were somewhat special since they originated from elliptic partial differential equations which appear in the theory of elasticity describing the static behavior under load e.g. of  plates. The asterisk means that the original array is transposed i.e. rows become columns and columns rows.