Matrix Tricks for Linear Statistical Models

1. Introduction
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

2. Easy Column Space Tricks
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

3. Easy Projector Tricks
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

4. Easy Correlation Tricks
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

5. Generalized Inverses in a Nutshell
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

6. Rank of the Partitioned Matrix and the Matrix Product
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

7. Rank Cancellation Rule
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

8. Sum of Orthogonal Projectors
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

9. A Decomposition of the Orthogonal Projector
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

10. Minimizing cov(y - Fx)
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

11. BLUE
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

12. General Solution to AYB = C
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

13. Invariance with Respect to the Choice of Generalized Inverse
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

14. Block-Diagonalization and the Schur Complement
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

15. Nonnegative Definiteness of a Partitioned Matrix
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

16. The Matrix dot{rm M}

Simo Puntanen, George P. H. Styan, Jarkko Isotalo

17. Disjointness of Column Spaces
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

18. Full Rank Decomposition
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

19. Eigenvalue Decomposition
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

20. Singular Value Decomposition
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

21. The Cauchy–Schwarz Inequality
Simo Puntanen, George P. H. Styan, Jarkko Isotalo

Keywords: Statistics, Statistical Theory and Methods