edX
edXApplications of Linear Algebra
384 studentsINTERMEDIATEEnglish
Korshub's take
Algebra Beyond Abstraction: Real Problems Solved
Linear algebra is powerful precisely because it translates real-world problems into mathematical form. This course shows you how, starting with Markov chains (modeling how systems change over time), progressing through eigenvalues and SVD, and culminating in optimization under constraints.
You'll see how Google uses linear algebra in PageRank, how least-squares regression fits models to noisy data, and how SVD reveals structure in massive matrices. The course builds your geometric intuition—understanding what these operations mean visually—not just the computational mechanics. By the end, you'll approach a new problem and recognize which linear algebra tool fits, whether it's spectral decomposition for optimization, QR factorization for numerical stability, or SVD for data compression and analysis.
About this course
Model and solve real-world problems using Markov chains, determinants, dynamical systems, and Google Page Rank. ,Construct the singular value decomposition (SVD) of a matrix and apply the SVD to estimate the rank and condition number of a matrix, construct a basis for the four fundamental spaces of a matrix, and construct a spectral decomposition of a matrix. ,Apply the iterative Gram Schmidt Process and the QR decomposition to construct an orthogonal basis of a subspace. ,Apply least-squares and multiple regression to construct a linear model from a data set. ,Apply eigenvalues and eigenvectors to solve optimization problems that are subject to distance and orthogonality constraints.
Price
$498
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