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Prove that trace of the matrix is invariant under similarity transformation?

The trace of an nxn matrix is usually thought of as the sum of the diagonal entries in the matrix. However, it is also the sum of the eigenvalues. This may help to understand why the proof works. So to answer your question, let's say A and B are matrices and A is similar to B. You want to prove that Trace A=Trace B If A is similar to B, there exists an invertible matrix P such that A=(P^-1 B P) Now we use the fact that Trace (AB)= Trace(BA) for any nxn matrices A and B.This is easy to prove directly from the definition of trace. (ask me if you need to know) So using this we have the following: Trace(A)=Trace(P^-1 B P)=Trace (BPP^-1)=Trace(B) and we are done! Dr. Chuck


Is trace Cyrus very good looking?

Yes trace Cyrus is extremely good looking!! =P


What is grade trace In medical terms?

Grade trace means a little bit.


What does it mean to Trace?

means to out line


What is it mean by 129 trace in aircraft parts traceability?

It means a trace back to airline.


99 Toyota Camry trouble code p 1133?

Trouble code P1133 means: Air-Fuel Sensor Circuit Response Malfunction


1999 Toyota Camry trouble code p 1133?

Trouble code P1133 means: Air-Fuel Sensor Circuit Response Malfunction


What rhymes with trace and means position?

place


What is trace pelviectasis?

Well I know pelvi = pelvis and ectasis = expansion but I don't know what trace means.


What does Trace A mean in a urinalysis?

Trace a means the first trait that shows up in DNA when talking about urinalysis


What plants response to water?

Thirsty Plants :p


Do police trace calls?

yep!!! so don't go callin 'um :P