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Two new tags and created in the same question by RougeSegwayUser. I think that they are not really needed, since and already exist.
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I am working through an applied category text. In it he makes several definitions: Definition 1: Let $(P, \leq)$ be a preorder. Then an upper set for P is a set such that if $p\in P$ and $p\leq q$, then $q\in P$. Definition 2: For a preorder as above, let $\uparrow a=\{p\in P | a\leq p \}$. ...

A new tag was created by Danilo Gregorin. The tag-info is empty.
In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev Nehari (1960, 1961). It is a differential manifold associated to the Dirichlet problem for the semilinear elliptic partial differential equation − △ u = | u | p − 1 u , with u ∣...
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In what follows, I transcribe an example that illustrates the application of the Nehari Manifold method to solve a nonlinear partial differential equation contained in the text (in Portuguese) that I am reading. My question is: Why can we conclude that $\Phi(u) \geq 0$ in the proof of Lemma 1.2 ...

A new tag was created by Rodrigo de Azevedo and added to 16 questions. He also created a tag-excerpt.
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When we want to define transformations using permutations, what are the subtle differencies betwen the use of permutation matrices, and the use of permutations? Say I want to define a way to shuffle a sequence of numbers. Shoud I define my transformation with permutation matrices, or only with t...

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The set $P$ of $n \times n$ permutation matrices spans a subspace of dimension $(n-1)^2+1$ within, say, the $n \times n$ complex matrices. Is there another description of this space? In particular, I am interested in a description of a subset of the permutation matrices which will form a basis....

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Just simple question: Can anyone provide a list of types of permutation matrices that commute (with the matrices of the same type)? for one, I can think of rotation matrix... (Oh, wait. it isn't really permutation matrix..)

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$\newcommand\mat{\mathbf}$A permutation matrix is a matrix whose columns are a permutation of the columns of the identity matrix $\mat I$. In other words, a permutation matrix is a matrix $\mat P$ with precisely one $1$ per row/column and zeros everywhere else. A few easy observations about per...

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Suppose I have a $n\times n$ matrix $A$. Can I, by using only pre- and post-multiplication by permutation matrices, permute all the elements of $A$? That is, there should be no binding conditions, like $a_{11}$ will always be to the left of $a_{n1}$, etc. This seems to be intuitively obvious. Wh...

Queries which show also editors who added/removed the tag: data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…