Chapter 1
Sturm’s Theorem
1.1 Sturm’s Thorem
Definition 1.1 We define that the number of changed sign V (a1, · · · , an) for
a = 1, · · · , an ∈ R is as follows.
For the sequense (a1, · · · , an), if ak = 0 (k = 1, · · · , n), we remove ak, and
the removed sequense is redefined (a1, · · · , am). Then we define that the number
of following elements
{i | aiai+1 < 0, 1 ≤ i