Question
The size of the blocks in this kind of matrix correspond to the algebraic multiplicity of its eigenvalues. For 10 points each:
[10h] Name this type of matrix, which consists of a series of eigenvalues with ones next to them.
ANSWER: Jordan canonical form [or Jordan normal form; Jordan matrix]
[10m] The importance of the Jordan canonical form comes from its resemblance to matrices with this form, such as the identity matrix. The equation A=PDP⁻¹ (“A equals P-D-P-inverse”) is used to convert matrices into matrices with this form.
ANSWER: diagonal
[10e] The Jordan canonical form is an “upper” example of this type of matrix, named for resembling a certain polygon. This type of matrix has all entries as 0s on one side of the diagonal.
ANSWER: triangular matrix [accept upper or lower triangular matrix]
<Benjamin McAvoy-Bickford, Other Science>
Summary
| 2023 Penn Bowl @ Waterloo | 10/28/2023 | Y | 2 | 30.00 | 100% | 100% | 100% |
| 2023 Penn Bowl @ FSU | 10/28/2023 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2023 Penn Bowl (Mainsite) | 10/21/2023 | Y | 4 | 20.00 | 100% | 50% | 50% |
| 2023 Penn Bowl (Norcal) | 10/28/2023 | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 Penn Bowl (UK) | 10/28/2023 | Y | 3 | 23.33 | 100% | 100% | 33% |
| 2023 Penn Bowl @ UNC | 10/28/2023 | Y | 2 | 20.00 | 100% | 100% | 0% |
Data
| Columbia B | Columbia A | 10 | 10 | 10 | 30 |
| UMD A | Cornell B | 10 | 10 | 10 | 30 |
| NYU | UMD B | 0 | 0 | 10 | 10 |
| Cornell A | Rutgers | 0 | 0 | 10 | 10 |