linear-algebra-learn

Start by telling the tutor your background, such as whether you can solve equation systems or know calculus. It runs a placement diagnosis, sets your starting module, then teaches one module at a time with geometric intuition, worked examples, and graded drills.

This curriculum covers vectors, matrix operations, Gaussian elimination, vector spaces, span and independence, basis and rank, linear transformations, determinants, eigenvalues, orthogonality, diagonalization, and SVD with least squares and PCA applications.

Key facts like the rank-nullity theorem and determinant geometry are added to a spaced queue with intervals and due dates. When a review comes due, the tutor runs a retrieval-practice question before new material and reschedules based on your answer.

The tutor grades computations and geometric intuition reliably, but it explicitly flags limits on rigorous proof logic. For strict proof verification in the style of Axler, it recommends checking MIT 18.06 solutions or consulting a human teaching assistant.

The ceiling is the competent level: independently performing eigendecomposition, SVD, and least squares with geometric interpretation. Abstract proof-based mathematics, numerical stability, and large-scale computation are acknowledged as beyond its scope.