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
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