Linear Algebra Practice

Instructions

1. Split the set across sessions.
2. Retry every hinted item independently.

Ordered items

1. Matrix fundamentals under time pressureLinear Algebra · 8 min
2. Basis, dimension, and coordinatesLinear Algebra · 8 min
3. Nullspace, column space, pivots, and block structureLinear Algebra · 14 min
4. Projection matrix as geometry and spectrumLinear Algebra · 15 min
5. Least squares, QR, and orthonormal projectionLinear Algebra · 18 min
6. Symmetry, orthogonality, and eigenspacesLinear Algebra · 16 min
7. Positive definite and semidefinite transformationsLinear Algebra · 14 min
8. Singular value decomposition from the Gram matrixLinear Algebra · 10 min
9. Low-rank error and explained varianceLinear Algebra · 8 min

Completion

Explain the algebraic and geometric meaning of rank, projection, eigenstructure, and SVD.