Unit 11 of 11
Applications and Review
- 2 lessons
- Videos 52 to 53
This unit applies the course to flows in a network and to fitting and reconstructing data from measurements.
An incidence matrix turns conservation at each node into a linear system, its kernel describes circulation around cycles, and requiring nonnegative flows adds constraints that go beyond the linear system. The review then chooses between least squares and a minimum-norm reconstruction, checks residuals and kernels, and separates agreement with the observed data from a validated model.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Network Flows
Network Flows, Conservation and Cycles
How a directed graph and its incidence matrix turn conservation at each node into a linear system with net supplies, how circulations around cycles span the kernel, and what nonnegative flows and the total supply condition add.
Video 52
Fitting and Reconstruction
Linear Algebra Review with Fitting and Reconstruction
How to tell an overdetermined fit from an underdetermined reconstruction, check residuals, choose the minimum-norm reconstruction, judge an added measurement, and separate agreement with data from a validated model.
Video 53