Praise for the First Edition

". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjoint matrix The Householder algorithm for turning self-adjoint matrices into tridiagonal form The compactness of the unit ball as a criterion of finite dimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.

Peter D. Lax 當代最傑齣的數學傢之一，世界數學界最高榮譽阿貝爾奬（2005年）和沃爾夫奬（1987年）得主。他是美國科學院院士，並於1986年榮獲美國國傢科技 奬章。Lax生於匈牙利，自1958年開始就一直在美國紐約大學從事教學與研究工作，曾擔任柯朗數學研究所所長。他在純數學與應用數學的諸多領域都有卓越 的建樹，影響深遠。同時，他一生緻力於數學教育，獨立撰寫或與他人閤著教材20多部，阿貝爾奬頒奬辭如此評價他：“他的著作、他對教育事業付齣的畢生心血 以及他在培養年輕一代數學傢時體現齣的孜孜不倦的精神，在世界數學領域留下瞭不可磨滅的影響。