Questions tagged [trace]

For questions about trace, which can concern matrices, operators or functions.

If your question concerns the trace map that maps a Sobolev function to its boundary values, please use [trace-map] instead.

In the context of linear algebra, the trace of a square matrix $M$ is the sum of the diagonal entries.

It's almost the same idea in the case of operators on a separable Hilbert space (with conditions of convergence).

In the context of partial differential equations, when we work with an open set having good conditions, we can define what we call a trace operator.

Use it with the appropriate tags.

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Trace of a $2 \times 2$ matrix

Let $\mathrm{A}$ a $2 \times 2$ matrix such that $\mathrm{I}\neq\mathrm{A}\neq\mathrm{-I}$, where $\mathrm{I}$ is the $2 \times 2$ identity matrix. If $\mathrm{A}=\mathrm{A}^{-1}$, find the trace of $\mathrm{A}.$
Harold
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