From 9fa6c4fd2d028299bff6dee0dd1719f70db355bc Mon Sep 17 00:00:00 2001 From: Matt <73741359+li1900@users.noreply.github.com> Date: Tue, 13 Aug 2024 12:57:49 -0400 Subject: [PATCH] correct a typo in line 398 (#432) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit the fourth vector should be [−2/3 -1/3 ]^T --- public/content/lessons/2016/change-of-basis/index.mdx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/public/content/lessons/2016/change-of-basis/index.mdx b/public/content/lessons/2016/change-of-basis/index.mdx index f3b82139..1d18a253 100644 --- a/public/content/lessons/2016/change-of-basis/index.mdx +++ b/public/content/lessons/2016/change-of-basis/index.mdx @@ -395,7 +395,7 @@ As a last step, apply the inverse change of basis matrix, multiplied on the left Since we could do this to any vector written in her language, first applying the change of basis matrix, then the transformation then the inverse change of basis, that composition of three matrices gives us the transformation matrix in Jennifer's language. It takes in a vector in her language, and spits out the transformed version of that vector in her language. -For this example, where Jennifer's basis vectors look like $\left[\begin{array}{c} 2 \\ 1 \end{array}\right]$ and $\left[\begin{array}{c} -1 \\ 1 \end{array}\right]$ to us, and we're translating a $90$ degree rotation, the product of these three matrices, if you work through it, has columns $\left[\begin{array}{c} 1/3 \\ 5/3 \end{array}\right]$ and $\left[\begin{array}{c} -2/3 \\ 1/3 \end{array}\right]$. So if Jennifer multiplies that matrix by the coordinates of a vector in her system, it will return the $90$ degree rotated version of her vector, expressed in her coordinate system. +For this example, where Jennifer's basis vectors look like $\left[\begin{array}{c} 2 \\ 1 \end{array}\right]$ and $\left[\begin{array}{c} -1 \\ 1 \end{array}\right]$ to us, and we're translating a $90$ degree rotation, the product of these three matrices, if you work through it, has columns $\left[\begin{array}{c} 1/3 \\ 5/3 \end{array}\right]$ and $\left[\begin{array}{c} -2/3 \\ -1/3 \end{array}\right]$. So if Jennifer multiplies that matrix by the coordinates of a vector in her system, it will return the $90$ degree rotated version of her vector, expressed in her coordinate system.