Unit 13: Change of basis
About this unit
The matrix P with the new basis vectors as columns turns new coordinates into standard ones and P⁻¹ turns them back; a transformation M becomes P⁻¹MP in the new basis.
By the end, you can: Convert coordinates between two bases with P and P⁻¹, and write a transformation in another basis as P⁻¹MP.
Modules
5 modulesLearn
- Same point, different numbersArticle · Coordinates depend on the basis; the matrix P whose columns are the new basis vectors turns new coordinates into ours, and P⁻¹ turns them back.Not started
- From screen to tilesWalkthrough · Use P⁻¹ to find a point's coordinates in the tilted basis, and check with P.Not started
- A transformation in tile coordinatesWalkthrough · Write a transformation in another basis as P⁻¹MP: convert in, apply, convert back, read right to left.Not started
- Translating between basesReview · Which matrix converts which way, and how a transformation looks in another basis.Not started