1. Introduction  
2. Linear Dimensionality Reduction as a Matrix Optimization Program  
2.1 Optimization Framework for Linear Dimensionality Reduction  
3. Survey of Linear Dimensionality Reduction Methods  
3.1 Linear Dimensionality Reduction with Orthogonal Matrix Constraints  
3.2 Linear Dimensionality Reduction with Unconstrained Objectives  
3.3 Scope Limitations  
3.4 Summary of the Framework  
4. Results  
4.1 Example of Eigenvector Suboptimality  
4.2 Performance Improvement  
4.3 Computational Cost  
4.4 Choice of Solver, and Identifiability  
5. Discussion