Trace

1 min read Updated Fri Apr 24 2026 03:19:45 GMT+0000 (Coordinated Universal Time)

Suppose A=(aij)n×nA=(a_{ij})_{n\times n} is an square matrix. Trace of AA is the sum of the diagonal entries.

trace(A)=Tr(A)=i=1naii\text{trace}(A)=\text{Tr}(A)=\sum_{i=1}^n{a_{ii}}

Trace is also equal to the sum of eigenvalues.

trace(A)=λi where λispectrum of A\text{trace}(A)=\sum{\lambda_i}\text{ where } \lambda_i \in \text{spectrum of } A