Linear Algebra and Advanced Matrix Topics

For multivariate statistics, we need to delve into more detail about matrices and other topics in linear algebra than is covered in Matrices and Iterative Processes. You don’t need to master all the topics described below, but it will be helpful to at least have a cursory knowledge of many of them. In any case, you may find you need to reference some of these topics when reading about multivariate statistics.

Topics

• Linear Independent Vectors
• Rank of a Matrix
• LU Decomposition
• Eigenvalues and Eigenvectors
• Orthogonal Vectors and Matrices
• QR Factorization
• Hessenberg Decomposition
• Symmetric Matrices
• Spectral Decomposition
• Positive Definite Matrices
• Cholesky Decomposition
• Singular Value Decomposition
• Pseudo-Inverse
• Schur’s Factorization
• Eigenvectors for Non-Symmetric Matrices
• Varimax Algorithm

References

Golub, G. H., Van Loan, C. F. (1996) Matrix computations. 3rd ed. Johns Hopkins University Press

Searle, S. R. (1982) Matrix algebra useful for statistics. Wiley

Perry, W. L. (1988) Elementary linear algebra. McGraw-Hill

Fasshauer, G. (2015) Linear algebra.
https://math.iit.edu/~fass/532_handouts.html

Lambers, J. (2010) Numerical linear algebra
https://www.yumpu.com/en/document/view/41276350