# Relationship between Translating Space and Translating Objects ## Translation of Grid When [translating](Translation.md) a circle, you need to keep in mind that you aren't actually translating the circle. You are actually translating the grid ($\mathbb{R}^2$) *underneath* the circle. ![](test.mp4) ## Change of basis vs. Matrix Transformations See more in [Rotation and Change of Basis](Rotation%20and%20Change%20of%20Basis.md). ### General Intuition The general take away is as follows: * In mathematics, we frequently are dealing with **objects/elements** * We always have a **system/structure/space** that we describe these elements with respect to * If we wish to transform the elements, we can equivalently think of this in two ways: > 1. Transform/map the elements themselves, keeping the space fixed > 2. Transform the space and leaving elements fixed * Either way, we can think of one these remaining fixed, and the other undergoing some transformation * --- Date: 20211107 Links to: [Mathematics MOC](Mathematics%20MOC.md) Tags: #review References: * [Original tweet I saw this at](https://twitter.com/i/status/1453393772314718215)