# Tagged Questions

**1**

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**0**answers

43 views

### For Finite Dual when is $(A \otimes A)^o = A^o \otimes A^0$?

Let $A$ be any $k$-algebra. The finite dual or restricted dual of $A$ is
$$
A^o = \{f \in A^* ~ | ~ f(I)= 0, \text{ for some ideal } I \subseteq A, \text{ such that } \text{dim}_k(A/I) < \infty\}.
...

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128 views

### Dimension of commutative subalgebras of a central simple algebra

let $k$ be a field, and let $A$ be a central simple $k$-algebra over $k$.
What is the maximal dimension of a commutative $k$-subalgebra of $A$?
If $A=M_r(D)$, where $D$ is a central division ...

**5**

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402 views

### A reference on semisimple linear algebra

Is there any literature where the tools familiar from (multi)linear algebra are systematically transferred to the setting of semisimple modules over noncommutative rings?
In fact this question is a ...

**5**

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**1**answer

1k views

### Algebra - Decomposition of a matrix polynomial

Dear All,
This is related with a problem that I'm trying to solve on my PhD dissertation in econometrics, and I thought that some mathmatician can know the answer.
What is known about a possible ...

**4**

votes

**1**answer

155 views

### Expressing a element of a Matrix subgroup in terms of subgroup generators

I'm no (computational) algebraist, and my searches have been pretty unyielding (probably due to the vast amounts written on the key words), but perhaps someone may know if this is possible, and if so, ...

**4**

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**1**answer

369 views

### A Question on Koszul duality and $B(\infty)$ structures on $HH^*$

The following theorem is known from a paper "Duality in Gerstenhaber Algebras" by Felix, Menichi, Thomas. Given a simply connected space X of finite type.
There is an equivalence of Gerstenhaber ...

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**0**answers

538 views

### Generalized Courant-Fischer theorem

Consider some quaternionic matrix $A$. A right eigvenvalue of $A$ is a quaternion $q$ such that $Ax=xq$ for some $x\in \mathbb{H}^n$. Similarly, a left eigenvalue of $A$ is quaternion $q$ such that ...

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**2**answers

368 views

### on existence of matrices X, Y s.t. XAY is diagonal over non-commutative ring

Given $A\in Mat_{n\times n}(R)$ where $R$ is a non-commutative associative ring are there exist any (non-zero) matrices $X, Y\in Mat_{n\times n}(R)$ such that $XAY=diag(a_1, \ldots , a_n)$ for some ...

**4**

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**1**answer

247 views

### Simultaneously orthogonally transform two SPD matrices to tridiagonal form?

Supposing you have two SPD matrices $A,B\in\mathbb{R}^{n\times n}$ are there any known results on the existence or non-existence of a unitary matrix $Q$ such that $Q^\top A Q=T_A$ and $Q^\top B Q=T_B$ ...

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2k views

### Left and right eigenvalues

A quaternionic matrix $A$ gives rise to a
function $\mathbb{H}^n \to \mathbb{H}^n$
given by $x \mapsto A \cdot x$. This is real linear,
but not complex- or quaternionic-linear
(in general) if we ...

**4**

votes

**2**answers

635 views

### Is there a name for this algebraic structure?

I found myself "naturally" dealing with an object of this form:
X is a complex vector space, with a "product" (a,b) → {aba} which is quadratic in the first variable, linear in the second, and ...