# Questions tagged [linear-transformations]

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. (Def: http://en.m.wikipedia.org/wiki/Linear_map)

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### Tensor Notation with Basis in Differential Geometry

Let's say we have two smooth riemannian manifolds $\mathfrak{B}$ and $\mathfrak{S}$ and with coordinates $X^A$ on $\mathfrak{B}$ and $x^a$ on $\mathfrak{S}$, with $A,a \in \{1,2,3\}$ Let's now assume ...
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### From cartesian to (discrete) skewed coordinate system

Some context. Let's say that I have a device made of "strips" for measuring positions. By strip device I mean that I have an area $H\times W$ (see figure a) which is made of elements (the ...
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### How to constrain a general mapping (from a multiset to a multiset) to a multirelation?

A multiset is a function, that assign a multiplicity (non-negative integer) to all elements of an underlying (universe) set. Let $A$ be a set, then $m: A \to \mathbb N_0$ is a multiset. $\mu A$ ...
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### For each $x\in X$, there exists $\lim_{n \to \infty}T_n x$ and introduce $T:X\to X$ as $Tx=\lim_{n \to \infty}T_n x\quad \text{for each } x\in X$.
Let $X$ be a Banach space and let $T_n \in \mathcal{B}(X)$ for each $n \in \mathbb{N}$. Assume that for each $x \in X$, there exists $\lim_{n \to \infty} T_n x$ and introduce the mapping $T : X \to X$ ...