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Matrix similarity
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This thesis will deal with similar matrices, also referred to as matrix conju-

gation.

The rst problem we will attack is whether or not two given matrices are

similar over some eld. To solve this problem we will introduce the Ratio-

nal Canonical Form, RCF. From this normal form, also called the Frobenius

normal form, we can determine whether or not the given matrices are sim-

ilar over any eld. We can also, given some eld F, see whether they are

similar over F or not. To be able to understand and prove the existence and

uniqueness of the RCF we will introduce some additional module theory. The

theory in this part will build up to nally prove the theorems regarding the

RCF that can be used to solve our problem.

The next problem we will investigate is regarding simultaneous conjugation,

i.e. conjugation by the same matrix on a pair of matrices. When are two pairs

of similar matrices simultaneously conjugated? Can we nd any necessary

or even sucient conditions on the matrices? We will address this more

complicated issue with the theory assembled in the rst part.

2

Place, publisher, year, edition, pages
2016. , 28 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-194214OAI: oai:DiVA.org:kth-194214DiVA: diva2:1038860
Available from: 2016-10-26 Created: 2016-10-20 Last updated: 2016-10-26Bibliographically approved

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