Physical behavior of eigenvalues and singular values in matrix decompositions

Abstract

An apposite as well as realistic treatment of eigenvalue and singular value problems are potentially of interest to a wide variety of people, including among others, design engineers, theoretical physicists, classical applied mathematics and numerical analysis who yearn to carry out research in the matrix field. In real world, it is extensively used but at sometimes scantily understood. This paper focuses on building a solid perception of eigenvalue as well as singular value with their substantial meanings. The main goals of this paper are to present an intuitive experience of both eigenvalue and singular value in matrix decompositions throughout a discussion by largely building on ideas from linear algebra and will be proficiently to gain a better perceptive of their physical meanings from graphical representation.