Trace of a 3x3 Matrix

$\text{Trace} = A11+A22+A33$

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The trace of an nxn matrix $A$ is the sum of the diagonal entries $A_11 , A_22 , ... , A_(n n)$ . So $tr(A)=sum_(i=1)^n A_(ii)$ .

For the 3x3 matrix
A = $[[A_11,A_12, A_13],[A_21,A_22,A_23],[A_31,A_32,A_33]]$ ,
the trace is given by $A_11 +A_22+ A_33$ .

The trace of a matrix is useful in determining the eigenvalues ( $λ_i$ ) of the matrix. For any matrix, $sum λ_i = sum A_(ii) = tr(A)$ .