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## [#20066] Existing page redirects to edit page with 'can't dup NilClass' error

Date:
2008-05-10 17:35
Priority:
3
Submitted By:
David Koenig (dmjkoenig)
Assigned To:
Nobody (None)
Category:
None
State:
Open
Summary:
Existing page redirects to edit page with 'can't dup NilClass' error

 Detailed description I have a page called Linear Transformations. When I go to it for the first time in a webrick session, it redirects to the edit page, as follows: 127.0.0.1 - - [10/May/2008:10:27:27 PDT] "GET /wiki/show/Linear+Algebra HTTP/1.1" 200 5459 http://localhost:2500/wiki/show/HomePage -> /wiki/show/Linear+Algebra 127.0.0.1 - - [10/May/2008:10:27:29 PDT] "GET /wiki/show/Linear+Transformations HTTP/1.1" 302 120 http://localhost:2500/wiki/show/Linear+Algebra -> /wiki/show/Linear+Transformations 127.0.0.1 - - [10/May/2008:10:27:29 PDT] "GET /wiki/edit/Linear+Transformations HTTP/1.1" 200 7862 http://localhost:2500/wiki/show/Linear+Algebra -> /wiki/edit/Linear+Transformations That edit page also has a "can't dup NilClass" error. If I edit that page, it goes back to normal afterward. The page contents are as follows (I've integrated jsMath into it, but don't think that's the problem): Each $(m \times n)$ matrix $A$ determines a function from $\mathbb{R}^n$ to $\mathbb{R}^m$ by $x \to Ax$. We will denote this map by $T$. That is, $T(x)=Ax$. For all $v,x \in \mathbb{R}^n,a \in \mathbb{R}$, * $T(v+w)=T(v)+T(w)$ * $T(av)=a\,T(v)$ **Definition**. Given two vector spaces $V, W$, a function $T : V \to W$ is a _linear transformation_ if for all vectors $u, v \in V$ and scalars $a \in \mathbb{R}$, * $T(u+v)=T(u)+T(v)$, and * $T(av)=a\,T(v)$. **Example**. Every $(m \times n)$ matrix $A$ is a map from $\mathbb{R}^n$ to $\mathbb{R}^m$. **Example**. On $C[a,b]$ define $T : C[a,b] \to C[a,b]$ by $T(f)(x)=\int_a^x f(t) \, dt$. **Example**. Let $C^\infty [a,b]$ be functions on $[a,b]$ that have derivatives of all orders. In this case, the derivation function $\frac{d}{dx}$ is a linear transformation. **Example**. Vector addition and scalar-vector multiplication in $\mathbb{R}^2$. **Non-Example**. Define a map $T : \mathbb{R}^n \to \mathbb{R}^n$ by $T(x)=x+b$, where $b$ is some fixed vector. Note that $T(2b) \ne 2T(b)$. **Facts**. * $T(0)=0$ * $T(-x)=-T(x)$. **Question**. Let $V$ be a vector space with with bases $\\{v\_1,\ldots,v\_n\\}$, $T:V \to W$. Suppose we know $Tv\_1,\ldots,Tv\_n$. Can we calculate $T\_x$ if $x\in V$? * Write $x=a\_1 v\_1 + \ldots + a\_n v\_n$. * So $T(x)=a\_1 Tv\_1 + \ldots + a\_n Tv\_n$. * So yes. **Theorem**. Every linear transformation $T:\mathbb{R}^n \to \mathbb{R}^m$ is given by multiplication by some $(m \times n)$ matrix $[Te\_1, \ldots, Te\_n]$. **Example**. In $\mathbb{R}^2$, rotation by $\theta$ is given by multiplication by $\left[\begin{matrix} \cos\theta & -\sin\theta\\\\ \sin\theta & \cos\theta \end{matrix}\right]$. The range of a linear transformation $T:V \to W$ is all vectors $w \in W$ such that there is some vector $v \in V$ such that $Tv=w$. The null space is defined as expected.