Lecture Notes for Linear Algebra

Lecture Notes for Linear Algebra provides instructors with a detailed lecture-by-lecture outline for a basic linear algebra course. The ideas and examples presented in this e-book are based on Strang’s video lectures for Mathematics 18.06 and 18.065, available on MIT’s OpenCourseWare (ocw.mit.edu) and YouTube (youtube.com/mitocw). Readers will quickly gain a picture of the whole course—the structure of the subject, the key topics in a natural order, and the connecting ideas that make linear algebra so beautiful. Preface 1 Textbooks, ZoomNotes, and Video Lectures 2 Three Great Factorizations : LU and QR and SVD 3 Part 1 : Basic Ideas of Linear Algebra 5 Part 2: Solving Linear Equations Ax = b : A is n by n 14 Part 3 : Vector Spaces and Subspaces, Basis and Dimension 21 Part 4 : Orthogonal Matrices and Least Squares 30 Part 5 : Determinant of a Square Matrix 35 Part 6 : Eigenvalues and Eigenvectors : Ax = λx and Anx = λnx 40 Part 7: Singular Values and Vectors: Av=σu and A=UΣV T 46 Part 8 : Linear Transformations and Their Matrices 54 Part 9 : Complex Numbers and the Fourier Matrix 59 Part 10 : Learning from Data : Minimize Loss by Gradient Descent 65 Part 11 : Basic Statistics : Mean, Variance, Covariance 72