### Table of contents:

1. Introduction to vectors;

2. Solving linear equations;

3. Vector spaces and subspaces;

4. Orthogonality; 5. Determinants;

6. Eigenvalues and eigenvectors;

7. The singular value decomposition (SVD);

8. Linear transformations;

9. Complex vectors and matrices;

10. Applications;

11. Numerical linear algebra;

12. Linear algebra in probability and statistics; Matrix factorizations; Index; Six great theorems/linear algebra in a nutshell.

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