# Tagged Questions

31 views

### Give a counterexample that $A$, $B$ are similar matrices in $M_{n\times n}(\mathbb{C})$ but $PAP^{-1}\neq B$ for any $P\in GL_{n}(\mathbb{R})$.

Give a counterexample that $A$, $B$ are similar matrices in $M_{n\times n}(\mathbb{C})$ but $PAP^{-1}\neq B$ for any $P\in GL_{n}(\mathbb{R})$. How to construct this example? I have obtained that of ...
117 views

### How to generate algebraic span of a set of matrices (how many multiplications?)

I've got a question about matrices and matrix algebras that offhand seems difficult, I'm wondering there is any sharp solution? Or perhaps it's known to not have any solution at all? Suppose you have ...
58 views

### differential equation of the square root of a matrix

If the differential equation governing the time dependent matrix $M(t)$ is $\frac{dM(t)}{dt}=A.M(t).B$ or $\frac{dM(t)}{dt}=A.M(t)+M(t).A$ where $A$ and $B$ are constant matrices, what is the ...
39 views

### Are decomposable maps completely bounded?

By the word decomposable I mean a positive map $\phi:\mathcal{B(H)}\rightarrow \mathcal{B(K)}$; $\mathcal{H,K~}$ are some Hilbert spaces and $\phi=\psi_1+T\circ \psi_2$ where $T$ is the transpose ...
46 views

### 2 positive decomposable maps

A positive map $\phi:\mathcal{B}(\mathbb{C}^n)\rightarrow\mathcal{B}(\mathbb{C}^n)$ is said to be $k$-positive if the natural extension ...
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### Composition of positive maps

Let $\chi_A:\mathcal{B}(\mathbb{C}^n)\rightarrow\mathcal{B}(\mathbb{C}^n)$ be a completely positive (cp) map defined as $\chi_A(x)=AxA^*$, where $A\in\mathcal{B}(\mathbb{C}^n)$. Clearly any cp map ...
128 views

### Basis for completely bounded maps.

The set of completely bounded (CB) maps forms can be considered as a complex span of the set of completely positive (CP) maps. Can we find a basis for this complex linear space of CB maps such that ...
923 views

### Taylor expansion for matrices

Is it possible to define a Taylor expansion for matrices ? Can I use functional derivative ? More precisely I have to calculate something like : $\ln(A+B)$ using a Taylor expansion, where $A$ and $B$ ...
I understand that an operator, $\hat{O}$, is said to be non-local if $$b(x)=\hat{O}a(x)=\int dx'O(x,x')a(x')$$ that is, to find $b(x)$ at aparticular value of $x$, we need to know ...