ABSTRACT
This chapter brießy reviews important concepts of linear algebra. We assume the reader already has some experience working with matrices, and linear algebra applied to solving simultaneous equations and eigenvalue problems. MATLAB has excellent capabilities to perform matrix operations using the fastest and most accurate algorithms currently available. The books by Strang [96] and Golub and Van Loan [47] give comprehensive treatments of matrix theory and of algorithm developments accounting for effects of Þnite precision arithmetic. One beautiful aspect of matrix theory is that fairly difÞcult proofs often lead to remarkably simple results valuable to users not necessarily familiar with all of the theoretical developments. For instance, the property that every real symmetric matrix of order n has real eigenvalues and a set of n orthonormal eigenvectors can be understood and used by someone unfamiliar with the proof. The current chapter summarizes a number of fundamental matrix properties and some of the related MATLAB functions. The intrinsic matrix functions use highly efÞcient algorithms originally from the LINPACK and EISPACK libraries which have now been superceded by LAPACK. [34, 42, 89]. Dr. Cleve Moler, the Chairman and Chief Scientist at The MathWorks, contributed to development of these systems. He also wrote the Þrst version of MATLAB. Readers should simultaneously study the current chapter and the MATLAB demo program on linear algebra.
