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>

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2023 Penn Bowl @ Waterloo10/28/2023Y230.00100%100%100%
2023 Penn Bowl @ FSU10/28/2023Y120.00100%100%0%
2023 Penn Bowl (Mainsite)10/21/2023Y420.00100%50%50%
2023 Penn Bowl (Norcal)10/28/2023Y215.00100%50%0%
2023 Penn Bowl (UK)10/28/2023Y323.33100%100%33%
2023 Penn Bowl @ UNC10/28/2023Y220.00100%100%0%

Data

North FloridaFSU B0101020