Linear Algebra for Chemometricians

Course Description

It has been said that "linear algebra is the language of chemometrics." Linear Algebra for Chemometricians provides the necessary mathematical background required to understand what's going on "under the hood" of most chemometric methods, and makes chemometric literature accessible. This half-day course introduces concepts that are required for a complete understanding of common techniques such as Principal Components Analysis, Partial Least Squares Regression, Multivariate Curve Resolution, etc.

Prerequisites

None, though this Primer On Linear Algebra is highly recommended.

Course Outline

1. Definitions: scalar, vector, matrix
   
2. Vector and matrix addition and multiplication
   
3. Inner products and projections
   
4. Outer products
   
5. Solving systems of equations
   
6. Matrix rank
   
7. Least squares
   
8. Ill-conditioned problems
   
9. Singular Value Decomposition (SVD)