This new fifth edition has become more than a textbook for the basic linear algebra course. That is its first purpose and always will be. The new chapters about applications of the SVD, probability and statistics, and Principal Component Analysis in finance and genetics, make it also a textbook for a second course, plus a resource at work. Linear algebra has become central in modern applied mathematics. This book supports the value of understanding linear algebra.

*Introduction to Linear Algebra, Fifth Edition* includes
challenge problems to complement the review problems that have
been highly praised in previous editions. The basic course is
followed by eight applications: differential equations in
engineering, graphs and networks, statistics, Fourier methods and
the FFT, linear programming, computer graphics, cryptography,
Principal Component Analysis, and singular values.

**Audience:** Thousands of teachers in colleges and
universities and now high schools are using this book, which
truly explains this crucial subject. This text is for readers
everywhere, with support from the websites and video lectures.
Every chapter begins with a summary for efficient review.

**Contents:** Chap. 1: Introduction to Vectors; Chap. 2:
Solving Linear Equations; Chap. 3: Vector Spaces and Subspaces;
Chap. 4: Orthogonality; Chap. 5: Determinants; Chap. 6:
Eigenvalues and Eigenvectors; Chap. 7: Singular Value
Decomposition; Chap. 8: Linear Transformations; Chap. 9: Complex
Vectors and Matrices; Chap. 10: Applications; Chap. 11: Numerical
Linear Algebra; Chap. 12: Linear Algebra in Probability and
Statistics; Matrix Factorizations; Index; Six Great Theorems.