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The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too.

Is there any geometric or physical (intuitive) significance related to the trace of a matrix?

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As @Amzoti and @Qmechanic suggested in the comments, the question has received satisfactory answers on MathOverflow and Physics Stack Exchange.

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