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Linear
Linear Algebra
Vectors, systems, maps, eigen. Later headings open after the one before. Work vectors, matrices, linear maps, and eigenproblems as a first linear algebra course does.
- 6 headings
- Ladder
- Test out a heading you have
Free to start. Sign in with Google or email.
A class on this path
Vectors and spaces · First class
Pick where you want to start
Each heading is its own course. Later ones open when you finish — or skip — the one before. A later course does not reteach earlier bands.
Vectors and spaces
Start hereDo linear combinations, span, and independence in R^n, and say when a set is a basis.
Matrices and systems
After Vectors and spaces — test out to unlockRow-reduce to RREF, read the solution set, and multiply matrices without losing the sizes.
Linear maps
After Matrices and systems — test out to unlockFind the matrix of a map, and compute kernel and image with the rank-nullity relation.
Determinants
After Linear maps — test out to unlockCompute a 2×2 and 3×3 determinant and say what invertibility and orientation have to do with it.
Eigenvalues
After Determinants — test out to unlockFind eigenvalues and eigenvectors of a small matrix, and diagonalise when it is possible.
Inner products
After Eigenvalues — test out to unlockCompute projections and least squares in R^n with the inner product, not with a black-box formula.
What this is for
- 01
Do linear combinations, span, and independence in R^n, and say when a set is a basis.
- 02
Row-reduce to RREF, read the solution set, and multiply matrices without losing the sizes.
- 03
Find the matrix of a map, and compute kernel and image with the rank-nullity relation.
Why a path, not a playlist
Vectors, systems, maps, eigen. Later headings open after the one before.
Each heading is its own course with a tutor. Later headings open when you finish — or test out of — the one before.
After you sign in
- •You land on this map — every heading is already there.
- •Take the open class, or test out of a later heading to unlock it.
- •Each heading is one shared course — same syllabus and first class for everyone. Later classes continue on your copy.