ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Binary cartesian set product
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Matrix main diagonal
Matrix trace
Definition D5945
Complex matrix trace
Formulation 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
The trace of $A$ is the D1207: Complex number \begin{equation} \text{Trace} A : = \sum_{n = 1}^N A_{n, n} \end{equation}
Children
Real matrix trace
Results
Trace of conjugate transpose equals conjugate of trace
Traces of complex matrix gramians coincide