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a12 an a2n a21 a22 Problem 2. Given an n x n matrix A = we define the trace of A, denoted : апn an2 anl tr(A), by n tr(A) = a

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m ut A = an m しin C12 m n mxn 48), (A8)-- (AB) xn nt AB = (Adha (A8)n xn tn1 (A 8) = Trace an, bin thnd n nk ban + Nar Let Rea bt4, 12- . +, im Trace (AB) + (&A)+leA - (A B)= (6A), Trace (AB) (&A) Tnace Trace - -. a A = N t caluwms Anm n X arthynd Th(ATA)22 A Then Trase (A AA) 11 + aie aie tナ a a2 + ae An2 -+ apmnm (AA) = Trace m tumes (AT A) = Trace Matrin 4rdhgen Noas,Alrcaly As we Remlt derdy True This (a), That is Pant Prncd (C trace (C Herre comrider = S, 0= AS Thur (s&A)=Tn (sAs) Trace

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a12 an a2n a21 a22 Problem 2. Given an n x n matrix A = we define the trace of A, denoted : апn an2 anl tr(A), by n tr(...
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