# Linear Algebra Practice

> ML preparation set.

- Stable ID: `linear-algebra-practice`
- Area: mathematics
- Kind: practice
- Timebox: 150 minutes

Cover matrix fundamentals, subspaces, projections, spectral structure, and decomposition.

## Instructions

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

## Ordered items

1. [Matrix fundamentals under time pressure](https://mlprep.iwase.dev/mathematics/linear-algebra/original-la-foundations/) — `original-la-foundations` (8 min)
2. [Basis, dimension, and coordinates](https://mlprep.iwase.dev/mathematics/linear-algebra/original-la-basis-change/) — `original-la-basis-change` (8 min)
3. [Nullspace, column space, pivots, and block structure](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam1-q2/) — `mit-18-06-s2010-exam1-q2` (14 min)
4. [Projection matrix as geometry and spectrum](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam2-q1/) — `mit-18-06-s2010-exam2-q1` (15 min)
5. [Least squares, QR, and orthonormal projection](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam2-q2/) — `mit-18-06-s2010-exam2-q2` (18 min)
6. [Symmetry, orthogonality, and eigenspaces](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam3-q1/) — `mit-18-06-s2010-exam3-q1` (16 min)
7. [Positive definite and semidefinite transformations](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam3-q2/) — `mit-18-06-s2010-exam3-q2` (14 min)
8. [Singular value decomposition from the Gram matrix](https://mlprep.iwase.dev/mathematics/linear-algebra/mit-18-06-s2010-exam3-q3c/) — `mit-18-06-s2010-exam3-q3c` (10 min)
9. [Low-rank error and explained variance](https://mlprep.iwase.dev/mathematics/linear-algebra/original-la-low-rank/) — `original-la-low-rank` (8 min)

## Completion

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