Linear Algebra for Everyone - Gilbert Strang

. .

Résumé :
This book by Gilbert Strang, author of the widely-used Introduction to Linear Algebra, presents a ``new start'' in teaching and learning linear algebra, a subject that is increasingly important in all quantitative disciplines. Working with small matrices of integers, students can see dependent columns and the rank of $A$ and its column space. This is a big step toward the four fundamental subspaces -- a widespread success in teaching linear algebra. The new start makes linear algebra more approachable to students with a wide range of backgrounds. The next step is the column-row factorization $A = CR$ with independent columns in $C$. Combinations of those columns produce all columns in $A$ -- this is matrix multiplication by $R$. The text goes on to solve $Ax = b$, to orthogonal bases, to subspaces and linear transformations, always based on examples. The final steps are eigenvalues and singular values, with a dedicated code to compress images. The last chapter is entirely optional: linear algebra in deep learning and AI. The text features many illustrative examples and exercises, and video lectures to accompany the book are available via MIT OpenCourseWare. The author's site, contains additional sample material and an instructor's manual....

Biographie:
Gilbert Strang has been teaching Linear Algebra at Massachusetts Institute of Technology (MIT) for over fifty years. His online lectures for MIT's OpenCourseWare have been viewed over ten million times. He is a former President of the Society for Industrial and Applied Mathematics and Chair of the Joint Policy Board for Mathematics. Professor Strang is the author of twelve books, including the bestselling classic Introduction to Linear Algebra (2016), now in its fifth edition....

Sommaire:
Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning....