Reorganize Chapter 3 (Linear Algebra)

[adowling2]

Challenges regarding Linear-Algebra-in-Numpy.ipnyb:

• The notebook is long
• The notebooks is a good starting point for graduate students in CBE 60258 to review first (because many have not taken linear algebra)

Proposed solution:

• Migrate the contents of the notebooks to a new chapter 3
• Remove the notebook from chapter 4 (now titled "Applied Linear Algebra")

Renumbered the chapters with PR #94.

Action items: create the following new notebooks for chapter 4 by deconstructing the current Linear-Algebra-in-Numpy.ipnyb in chapter 4. (First make the new notebooks, then we can delete this notebook from chapter 3.)

• Notation and Matrix Operations
• Determinant
• Matrix Inverse
• LU Decomposition
• Eigendecomposition
  • Definition
  • Visualization of stretching (Wikipedia?)
  • Calculation procedure (characteristic equation)
  • Curvature of a second order polynomial (definiteness)
  • Orthagonalize matrix (change of basis, e.g., covariance)
• Singular Value Decomposition
  • Definition
  • Calculation procedure
  • Add data compression example from MATLAB days of CBE 20258 (or find image compression example online)
  • Find SVD example problems from MATLAB days of CBE 20258
• Diagnosing Near Singular Linear Systems
  • Eigendecomposition of A and A^T to find how to add rows and columns to determine degeneracy
  • SVD, interpret left and right singular vectors

Notebooks to Add Later (AD):

• Cholesky Decomposition
• QR Decomposition