In the Analysis2 midterm exam, we had the following problem: Let the equation anxn+⋯+a1x+a0=0anxn+⋯+a1x+a0=0 has nn simple real roots (distinct) {α1,⋯,αn}{α1,⋯,αn}. Prove that the above equation has still nn distinct real roots when the ch...
Finally, the invert colors technique can be useful for highlighting specific features or patterns in the photo that couldn't otherwise be noticed due to the dark areas. Luckily, the invert filter makes the dark areas light in the final inverted image, and you can always revert back if needed...
So, the total explained variance of equals , meaning we lost 20% of the original variance. That amount of lost information can be critical for some applications. If we ran PCA with four PCs, the dimensionality would remain unchanged, and we could reconstruct the data precisely. 5. ...
When 𝛼α is excessively small, the inversion model tends to fit the observation data effectively and with a small constraint effect, which may induce over-fitting of high-frequent noise in the observation data. As a result, the solution of target function loses physical meaning because of ...