All Questions
Tagged with linear-algebra fields
7 questions with no upvoted or accepted answers
2
votes
0
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59
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Tensor product of two transcendental flat algebras is not a field?
I'm considering the correctness of the following assertion, which is related to linear disjointness (I'm trying to generalize it to subalgebras), What does "linearly disjoint" mean for ...
- 173
2
votes
0
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92
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System of linear equations in positive characteristic
Let $K$ be a field of positive characteristic $p$. Consider the system of $\mathbb F_p$-linear equations
$$\left\{\begin{array}{ccl}
a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n&=&b_1\\
a_{11}x^p_1+a_{...
- 3,998
2
votes
0
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214
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Is there a symmetric basis for $\mathbf{Q}(x,y)$?
Consider $\mathbf{Q}(x,y)$, the rational functions in $x$ and $y$, as a vector space over $\mathbf{Q}$.
Let $\sigma$ be the map interchanging $x$ and $y$. Is there a basis for $\mathbf{Q}(x,y)$ ...
user44143
1
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0
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246
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Frobenius twist of a field
Let $k$ be a field of characteristic $p>0$ (not necessarily perfect). Consider the Frobenius endomorphism $F : k \to k$, $x \mapsto x^p$. I am curious about what happens when we take $k$ as a $k$-...
1
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268
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Determinant and restriction of scalar
Let $E/F$ be a finite separable extension of fields, and $V$ a finite dimensional vector space over $E$. Let $T\in\operatorname{End}_EV$ be a linear operator on $V$, and let $\det(T)$ be its ...
- 833
1
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0
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107
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Complementation in an extension field
If $E$ is an extension field of $F$, is $F$ necessarily (without assuming the axiom of choice) complemented as a vector subspace of $E$? (Of course the answer is easily yes if the extension is finite....
- 11.4k
0
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108
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Generalization of SVD algorithm
Let $K$ be a field, $A\in K^{n\times m}$ and $\lVert \cdot \rVert$ the Euclidean norm. Consider the problem: Find a $v\in K^m$ such that
\begin{align}
\lVert Av\rVert=\min_{\lVert x\rVert=1}\lVert Ax\...
- 157