# Questions tagged [trace]

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

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### Why does the trace show up in such expressions?

I've been studying different scattering processes (from Mandl & Shaw QFT's book, chapter 8) and there's always a purely-mathematical common step I do not understand: the showing-up of the trace. ...
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### How to prove that if $A$ is a square matrix on $\mathbb{R}$, $A$ is nilpotent, then trace($A$)=0

I need some help, I need to prove the following: Let $A$ be a square matrix on $\mathbb{R}$, if $A$ is nilpotent then Trace($A$)=0 I have seen some results for complex entries of the matrix, but what ...
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### Lower bound on determinant of difference of matrices

Are there any lower bounds on the $\det(I+A^\top A - B^\top B)$? I'm looking for a bound that possibly depends on the 2-norm, Frobenius norm, or trace of $A$ and $B$. My attempt: Let $\lambda_i$ be ...
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### How do you compute the partial trace in the oblique coordinates $a=u+\frac{1}{2}x, b=x$?

For my master's thesis I am reading the paper https://arxiv.org/abs/1204.5627 about quantum reference frame changes to center of mass coordinates. On Page 4, there is a calculation i just can't make ...
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### Mistake in Rasmussen & Williams 2006 or my mistake?

I wonder if I make any stupid mistake understanding this, or can there actually a mistake in the bible of Gaussian Processes: Rasmussen & Williams 2006: Gaussian Processes for Machine Learning? ...
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### What sort of matrix norms bound traces of products?

Suppose I have some linear operators $X_1, \dots, X_n$ on $\mathbb{C}^r$ (i.e. $r \times r$ matrices) and some other operators $Y_1^\epsilon, \dots, Y_n^\epsilon$ which are deformations of the $X_i$, ...
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### Trace matrix calculation

The square of the Frobenius norm of an $n\times d$ matrix $X$ is equal to Tr($X^TX$). $$||X||_F^2 = \mathrm{Tr}(X^TX).$$ Then in the case of matrix involving addition or subtraction would be, for ...
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### Please I need help for this problem if ABA=0 then tr(AB)=0 [closed]

A, B are nxn matrices if ABA=0 then tr(AB)=0
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### Modifying circulant Latin Squares

Question: Given a $N \times N$ circulant Latin square, $M$, is there a sequence of algorithmic modifications that one can make to $M$ such that the main diagonal will consist of exactly $2$ distinct ...
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### Derivatives of trace of complicated function

When $A$, $B$ and $C$ are positive semi-definite and hermitian symmetric matrices, what is the derivative and second derivatives of $f(x) = tr(x^2 A (xB + C)^{-1})$, for $x>0$ ?
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### Why sometimes the trace of a inverse matrix is very high and sometimes is low?

I have an implementation that produces a matrix $A$. I am working on the trace of it's inverse $tr(A^{-1})$. In my problem, there are just two states for the result. Sometimes the result is very high ...
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### Relate l1 norm of Hadamard product to trace

Suppose $A$ is a $q\times p$ matrix, $B$ is $q \times p$ matrix, $A_j$ is the jth column of $A$, and $B_j$ is the jth column of $B$. The following sum of $l_1$ norms, where "$\circ$" is the ...
I am studying algebraic number theory and I am having trouble understanding something. Let $K$ be a number field with ring of integers $\mathcal{O}_K$. Suppose a prime $p$ does not ramify in $K$. Then ...
### A linear transformation such that $T(AB)=T(BA)$
The question goes as follows: Let $V$ be a vector space and let $T: M_{2 \times 2} (R) —> V$ such that $T(AB)=T(BA)$ for all $A, B \in M_{2 \times 2}$. Show that $T(A) = 1/2(trA)T(I2)$ for all \$A \...