1. Show that two matrices A,B ∈ Mn(C) are similar if and only if they share a Jordan canonical form.(adsbygoogle = window.adsbygoogle || []).push({});

2. Prove or disprove: A square matrix A ∈ Mn (F) is similar to its transpose A^{T}. If the statement is false, ﬁnd a condition which makes it true.

(I'm pretty sure that this is true and can be proven using the above by showing that A and A^{T}share a Jordan form.)

I have a basic understanding of what Jordan blocks are and what JCF matrices look like, but I don't know what the identifying characteristics of a specific JCF are or how to show that two arbitrary matrices share the same form. I know in both questions that the two matrices have the same characteristic polynomial and spectrum, but I don't know where to go from there.

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# Homework Help: Jordan canonical form

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