# 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.

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### If $\operatorname{trace}((cI+A)^{-3}A(cB-2I))<0$, is it true that $\operatorname{trace}((cI+A)^{-4}A(cB-2I))<0$?

Given a nonnegative scalar $c$, two positive definite matrices $A$ and $B$, if $\operatorname{trace}((cI+A)^{-3}A(cB-2I))<0$, is it true that $\operatorname{trace}((cI+A)^{-4}A(cB-2I))<0$?
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### Non-scalar quadratic forms with non-PSD and non-Hermitian coefficient matrices

I need to implement the expression $obj = \mbox{tr}(AXB'Y'A'X'BY)$ in CVX, where $A$ and $B$ are known complex matrices and $X$ and $Y$ are unknown complex matrices, which I intend to optimize $X$ ...
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### Upper bound on trace for powers of a matrix which converges to zero

For some fixed square matrix $X$ for which $\lim_{n\rightarrow\infty} X^n = 0$, it is apparent that the trace of $X^n$ must also converge to zero as $n\rightarrow\infty$. Is there anything I can do to ...
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### Trace of a power of a skew-symmetric matrix

How to express ${\rm Tr}(A^n)$ (in terms of ${\rm det}\,A$), where $A$ is a skew-symmetric $m\times m$ matrix? With references if possible.
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### Simplification of a Partial Trace

After some derivations, I arrived at the following result. Given the following matrices $\mathbf{C}_{ij}\in R^{n\times n}$, $i,j\in[1..m]$ and the diagonal matrix $\mathbf{Q}\in R^{n\times n}$, I have ...
1 vote
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### Projection of tensor in vectorial space

Let us consider the closed convex cone of Sym (Sym be the subspaces of Lin constituted by all symmetric tensors) K={A∈ Sym such that trA ≤ 0 } For each E∈ Sym determine the projection P(E) of E onto K
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### trace Inner product

Attempt I have come across this sequence of questions whilst revising for my linear algebra exam,I have tried to answer these questions (with my attempt attached) but I am in no way sure that I have ...
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### Multiplicative property of trace

Let $T_1 \in \mathcal{L}(V)$ and $T_2 \in \mathcal{L}(V)$ be positive operators. Prove that the trace of their product is non-negative i.e., tr($T_1 T_2) \geq 0$ Attempt 1: Obviously, a positive ...