Least Norm | Practical Linear Algebra (Lecture 9)

Time for some least norm. Prepare to have your mind blown. Here we learn about underdetermined systems, take a geometric look at norm minimization, introduce Lagrange multipliers, derive the closed-form solution for the least norm problem, and explore bioelectromagnetics as an incredibly interesting and useful application. Find all the slides here: https://github.com/rmislam/practical-linear-algebra Find the full official playlist for this series here: https://www.youtube.com/playlist?list=PL8M_xnXITgpojyYsYUNgxbkOEPCvwsrCm Paper on the minimum norm estimate in EEG/MEG analysis by Olaf Hauk: https://www.researchgate.net/publication/8649556_Keep_it_simple_A_case_for_using_classical_minimum_norm_estimation_in_the_analysis_of_EEG_and_MEG_data MNE-Python: https://mne.tools/stable/index.html FieldTrip: https://www.fieldtriptoolbox.org/ Great talk on EEG/MEG by Prof Hamalainen: https://www.youtube.com/watch?v=VDmRsz3Vl2Q Great talk on EEG/MEG by Prof Oostenveld: https://www.youtube.com/watch?v=86f5_x9SVQQ Figures taken from these excellent papers: Naess et. al., “Biophysically detailed forward modeling of the neural origin of EEG and MEG signals” https://www.sciencedirect.com/science/article/pii/S1053811920309526?via%3Dihub Hagen et. al., “Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0” https://www.frontiersin.org/articles/10.3389/fninf.2018.00092/full