Trace(Trace A) for A matrix

Question

Is there any known meaning of $$Tr(Tr A)$$ where A is a $n \times $n matrix

Trace is defined as the (scalar) sum of the elements in the main diagonal of a square matrix. Taking the trace of a scalar is meaningless unless you "cheat" and imagine it as a $1\times1$ square matrix. Then the trace is the scalar itself. — Scene, May 04 '24 at 21:00

msantama · Answer 1 · 2024-05-04T21:10:44.163

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For all $A \in \mathbb{R}^{n \times n}$ it holds that

$$\mathsf{tr}\left( \mathsf{tr}\left( A \right) \right) = \mathsf{tr}\left( A \right)$$

The trace operator outputs a scalar and the trace of a scalar is a no-op.

edited May 04 '24 at 21:10

answered May 04 '24 at 20:55

msantama

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Trace is only defined for square matrices. – José Carlos Santos May 04 '24 at 21:05
Right, thanks. It should read $A \in \mathbb{R}^{n \times n}$ – msantama May 04 '24 at 21:10
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No, you did not. – José Carlos Santos May 04 '24 at 21:10
How about Tr(A /Tr(A))? – Ankush May 04 '24 at 22:07
Use the property that $\mathsf{tr}(cA) = c\mathsf{tr}(A)$ for any scalar $c$ – msantama May 04 '24 at 22:10
could you suggest something on "https://physics.stackexchange.com/q/812241/401303" this too – Ankush May 05 '24 at 18:25

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