Question
The fact that the Rayleigh quotient is bounded between the smallest and largest of these quantities is elaborated upon by the min-max theorem. For 10 points each:
[10m] Name these quantities, the set of which is the spectrum. The trace equals the sum of these quantities, which are the roots of the characteristic polynomial.
ANSWER: eigenvalues [prompt on lambda; prompt on characteristic value or characteristic root]
[10e] Eigenvalues describe these rectangular grids of numbers that represent linear transformations.
ANSWER: matrices [or matrix]
[10h] This task, which factors a matrix into the product of a unitary matrix, a diagonal matrix denoted "Sigma," and the conjugate transpose of a unitary matrix, is named for the square roots of the non-negative eigenvalues that populate Sigma.
ANSWER: singular value decomposition [or SVD; prompt on decomposition]
<Science - Other Science - Computer Science>
Data
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 36 | 11.94 | 86% | 28% | 6% |