Trace of a Matrix

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The sum of diagonal elements of a square matrix A is called the trace of a matrix A, which is denoted by tr A.

trA = \sum\limits_{i = 1}^n {{a_{ii}}}

Properties of trace of a matrix :

(i) tr(λA) = λ tr(A)

(ii) tr(A – B) = tr(A) – tr(B)

(iii) tr(AB) = tr(BA)

(iv) tr(A) = tr(A’)

(v) tr(In) = n

(vi) tr(0) = 0

tr(AB) ≠ tr(A).tr(B)

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