Consider the 4x4 matrices(adsbygoogle = window.adsbygoogle || []).push({});

A =

(1 2 3 4)

(5 6 7 8)

(9 10 11 12)

(13 14 15 16)

B=

(1 2 3 4)

(8 5 6 7)

(11 12 9 10)

(14 15 16 13)

The question I was asked was the following: Show that there does not exist an endomorphism f: ℝ^{4}-> ℝ^{4}and basis 'a' and 'b' of R^4, such that A =_{a}[f]_{a}and B=_{b}[f]_{b}.

I have read in my notes and found that if the traces of the two matrices are not the same then they cannot represent the same endomorphism.

I am struggling to see the intuition behind this though.

Can anyone shed some light?

Many thanks

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# Trace and endomorphism

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