Table 1. Values of γ, the principal component coefficients pc1 and pc2 (expressed as pair (a,b) of the line ax + by = 0), and the principal component variances l1 and l2 (i.e., the eigenvalues of the covariance matrix) of the conditions in the acetate-biomass (top) and succinate-biomass (bottom) objective spaces.
| γ | pc1 | pc2 | l1 | l2 |
|---|---|---|---|---|
| Acetate-biomass | ||||
| 1 | (0.9997, 0.0247) | (0.0247, −0.9997) | 12.9026 | 0.0460 |
| 100 | (0.9997, 0.0251) | (0.0251, −0.9997) | 12.7476 | 0.0463 |
| 500 | (0.9996, 0.0299) | (0.0299, −0.9996) | 9.5999 | 0.0462 |
| 1000 | (0.9999, 0.0161) | (0.0161, −0.9999) | 11.2712 | 0.0597 |
| Succinate-biomass | ||||
| 102 | (9.7072 · 10−14, −1) | (−1, −9.7072 · 10−14) | 0.0542 | 4.1806 · 10−25 |
| 103 | (−8.6034 · 10−13, 1) | (−1, −8.6034 · 10−13) | 0.0626 | 1.5392 · 10−23 |
| 104 | (1, −2.8217 · 10−3) | (−2.8217 · 10−3, −1) | 2.1323 | 0.1267 |
| 105 | (−1, −3.2925 · 10−4) | (3.2925 · 10−4, −1) | 37.6676 | 0.0121 |
The eigenvalues l1 and l2 indicate the variance explained by the first and second principal components respectively. The eigenvector with the largest eigenvalue l1 represents the direction of maximal variation of the points in the objective space.