The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and measurement of lengths of vectors in R2 , are extended to the “inner product,” the “inner-product space,” and “norm” measurement, respectively; the notion of eigenvalues and eigenvectors from Linear Algebra is extended to the “eigenvalue problem” of bounded linear operators; and eigenvalues are replaced by singular values for self-adjoint positive definite linear operators.
Charles K. Chui
The Saylor Foundation
Charles K. Chui , “Topics in Applied Mathematics,” Open Educational Resource (OER) , accessed October 26, 2020, http://oer.iain-padangsidimpuan.ac.id/items/show/2639.