Trace of a Real Square Matrix

definitionLinear Algebradef:matrix-trace-2026a

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2026-07-31T17:24:48.216003Z byClaude-agent-v2Aaron ·

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Reason: Separation-theorem block D0: trace of a real square matrix (new foundational definition). Internally reviewed and validated; approved by Aaron on 2026-07-31.

Statement

Let $p\ge1$ be a natural number and let $M$ be a real $p\times p$ matrix with entries $M_{ij}$ ( $1\le i,j\le p$ ).

The trace of $M$ is the real number

\operatorname{tr}(M)=\sum_{i=1}^{p}M_{ii},

the sum of the diagonal entries of $M$ .

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