Channel: Looking Glass Universe

Category: Science & Technology

Tags: change of basiscoordinate systemchange of basis vectorschange-of-basischange of basis linear transformationchange of basis matrixchange of coordinates linear algebrachange of basis matriceschange of base formulatransition matrixchange of basis linear algebracoordinate system transformation examplechange of basis examplechange of basis linear algebra examplestransformation matrixvector spaces and subspaceslinear algebra

Description: This video is part of a linear algebra series: Vectors and Bases: youtu.be/3ZfrJ0Sk5iY Matrices and Linear Transforms: youtu.be/CBIO4xJ1Cok Matrix inverses: youtu.be/ESKcF8XFzLM This video is about changing the basis (or coordinate system) of a matrix or a vector. While the change of basis formula is often presented as something to just memorise, we'll see it's actually very very straightforward to understand. Hints for homework: 1. You can do it! Think about what it does to the basis vectors! 2. Remember, in the original case you first translate the input vector from Bob's basis to Alice's so you can apply M_a, then translate back. A similar idea applies, but you need to translate to something M_a can take as input. Answers to homework below!!! Answers The answer to question one is 2. The answer to question two is 3.