On the OCW page for 18.06 Linear Algebra (Spring 2010) , you will find a section titled “Readings.” This contains for each session. These are dense, precise, and serve as the script for the video lectures.
The SVD is widely used in modern computer science for Principal Component Analysis (PCA), image compression, and recommendation algorithms. Gilbert Strang's Golden Rules Summary
For further study, watch his MIT OpenCourseWare lectures (18.06), work through the problem sets, and experiment with Python (NumPy) to see these concepts in action. lecture notes for linear algebra gilbert strang
Mastering Linear Algebra: A Guide to Gilbert Strang’s Legendary Lecture Notes
From these properties, we derive that a matrix is invertible if and only if The Eigenvalue Equation Eigenvalues ( ) and eigenvectors ( On the OCW page for 18
When (Ax = b) has no solution, we solve (A^TA\hatx = A^Tb). This minimizes (|Ax - b|^2). The least squares solution is: [ \hatx = (A^TA)^-1A^T b ]
." This mental shift makes matrix algebra much easier than the standard "row times column" dot product method. Gilbert Strang's Golden Rules Summary For further study,
After elimination, the system is upper triangular. Solve from the bottom up.
For over two decades, Strang's method has succeeded where many others failed because of a few key principles: