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Results tagged with matrices
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user 16739
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
1
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1
answer
247
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characterize certain type of matrices
I am trying to characterize matrices with a certain property :
Define $U$ as an $n \times n$ matrix (over C or R; you can also assume
that it is unitary or orthogonal if it helps). … In the case of $n=2$ this would put
a restriction on $U=((a,b),(c,d))$ : $ad+bc=0$; and $y_1y_2$ would be $c_1x_1^2+c_2x_2^2$; My question
is : are such matrices known in the literature by some name? …
- 451
1
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0
answers
154
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When can a binary matrix be transformed into a certain form
I have a $k \times n$ matrix $G$ over ${\mathbb F_2}$ that's full rank.
This can always be put in systematic form : $G \sim [I_k \mid P]$ where $I_k$ is a $k \times k$ identity matrix and $P$ is a $k …
- 451
9
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1
answer
302
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a generalization of gamma matrices
Is it possible to find matrix solutions to the following :
$$\left(\sum_1^m M_k x_k\right)^n=\left(\sum_1^m x_k^n\right)I_d$$
where $M_k$ are the desired $d \times d$ matrices (no restriction on $d$) and … $x_i$ are indeterminate variables;
For n=2 the gamma matrices satisfing $M_i M_j + M_j M_i = 2\delta_{ij}$ work; so in a way this is a generalization of these to larger $n$. …
- 451
5
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2
answers
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Decomposing a matrix into a product of sparse matrices
How to study the decomposition of a square matrix into a product of sparse matrices?
There are no restrictions on the number of matrices in the product, but the fewer the better. …
- 451