# Tagged Questions

129 views

### Dimension of a commuting nilpotent variety

Fix $k$ an algebraically closed field, $n$ a natural number, and $\lambda=(\lambda_1,\ldots,\lambda_m)$ a partition of $n$. Let $A$ be any $n\times n$ nilpotent matrix with entries in $k$ whose ...
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### How to maximize the determinant of a matrix of the form VDV^H

Hi, I have a matrix of the form $A=VDV^H$, where $V$ is a $M \times 2M$ complex matrix, $D$ is a $2M \times 2M$ diagonal real matrix, thus the dimension of $A$ is $M \times M$. My problem is how ...
310 views

### Checking for invertibility of large matrices in MAGMA

If you have a number of large matrices, and you wish to determine whether each matrix has determinant zero or not, what is the most efficient way to do this in MAGMA (it appears that calculating the ...
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### Basis of a Finite Dimensional Algebra with a Finitely Generated Relation Set By Computer

Let $A$ be a noncommutative finitely generated algebra with a finitely generated set of relations. Moreover, assume that $A$ is finite dimensional as a vector space. What I want to know is, can ...
1k views

### Computer algebra system for calculation of characteristic polynomial of sparse matrix

I have a $n \times n$ matrix, for which i need to calculate the characteristic polynomial. The matrix is over $GF(2)$, and $n \approx 10^4$. However the matrix is very sparse, with around $n$ non ...
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### Constructing a unitary matrix

Setting: Given a set of $n\times n$ matrices $A_i$, I would like to find a linear combination of these matrices $Q = \sum_i A_i x_i$ with $x_i$ a set of complex numbers, such that $Q$ is unitary: ...
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### 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, ...
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### Algorithm/denominators of elements of a rational affine space

I hope it's not a trivial question... Suppose I have a finite dimensional vector space $V$ over $\mathbb{Q}$ with a distinguished basis (in my case it's the $k$th graded piece of the free associative ...