Trace equals the sum of true eigenvalues

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For any finite square matrix, the trace is the sum of its eigenvalues counted with algebraic multiplicity. The method correctly sums the stored diagonal. This identity supplies a quick consistency check against a proposed complete eigenvalue list, and the source’s separate trigonometric lists fail it for the default intra- and inter-strand matrices.

Terms & definitions

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Original context

        for (double e : spectrum) {
            int bin = std::min(static_cast<int>((e - min_e) / bin_width), num_bins - 1);
            dos[bin]++;
        }
        return dos;
    }

    // Trace (sum of eigenvalues = sum of diagonal)
    double trace() const {
        double tr = 0.0;
        for (int i = 0; i < TOTAL_BONDS; ++i) {
            tr += M_[i][i];
        }
        return tr;
    }

    const auto& matrix() const { return M_; }
    const IntraStrandBlock& intra_block() const { return intra_; }

Trace (sum of eigenvalues = sum of diagonal)

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