ABSTRACT
This chapter introduces the A Programming Language (APL) functions for multiplying matrices, solving systems of equations, generating least-squares solutions of systems, computing matrix inverses, and transposing matrices. It presents examples of significant mathematical uses. The chapter addresses the generalized inner product and reviews the outer product. It considers these operators in the examples and exercises. Multiplication of matrices can be presented as an extension of the dot product of vectors. To solve linear algebraic systems with APL, it is convenient to view them in vector-matrix form. Systems having the same coefficient matrix but different right-hand side vectors can be solved simultaneously by forming the right-hand side vectors into a matrix and using domino as before. Many matrix algebra computations involve transposes of matrices. It is usually difficult to attack the problem of finding the eigenvalues of a matrix by directly computing the characteristic equation and locating its roots.
