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1 Introduction to Vectors

2 Solving Linear Equations

3 Vector Spaces and Subspaces

4 Orthogonality

5 Determinants

6 Eigenvalues and Eigenvectors

7 Linear Transformations

8 Applications

9 Numerical Linear Algebra

10 Complex Vectors and Matrices

This International Edition shares the website math.mit.edu/linearalgebra with the US edition.
I hope the video lectures on MIT’s OpenCourseWare are helpful to students and faculty (Math 18.06 and 18.06SC on ocw.mit.edu). Now Kyobo Books has made it possible to teach directly from the textbook for that course.
May I mention a new data science feature of the International Edition. The last pages of the book have developed from my new MIT course 18.065 and its textbook : Linear Algebra and Learning from Data(2019), Wellesley-Cambridge Press, ISBN 9780692-19638-0. I hoped for many years that MIT could have
a second course on applied linear algebra. With the amazing growth of machine learning and artificial intelligence, this new course became possible. More than 100 MIT students from all years and all departments choose this course every spring. 18.065 is now included with video lectures on OpenCourseWare ocw.mit.edu. The new textbook has the website math.mit.edu/learningfromdata.
The key ideas of deep learning are now included in the Appendix to the International Edition that is available in Taiwan and Korea.
The reader learns how to construct a function F(x,v) that gives the correct output on the known training data v. In image recognition F gives the correct classification of the image.
The vector x of weights contains the matrices that multiply v to give that output.
The learning function F must be nonlinear ! Each new layer includes ReLU(v) = max (0,v). Nonlinearity is responsible for the success of deep learning.
The International Edition contains my SIAM News article (December 2018) about the detailed structure of F(x,v). The “magic success” is that F also gives the correct classification for data it has not seen.
This new part of the textbook opens up a major application of linear algebra. All professors and teachers
will know that the heart of the textbook is linear algebra. This subject has jumped forward in importance for many parts of mathematics, linear algebra is as essential as calculus.