What are some books that focus on the more intuitive part of linear algebra study?So far only this series of lessons have been satisfactory, but they are very consice, and the books that I have come across so far focus on a more rigorous definition of linear algebra that start with solving equations. Where and how could I get a more geometrically interpretable study for linear algebra?
This clear, concise and highly readable text is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focusses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions. From the very start, linear algebra is presented as an extension of the theory of simultaneous linear equations and their geometric interpretation is shown to be a recurring theme of the subject.
Linear Algebra A Geometric Approach By S Kumaresan
Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms.
The classical paradigm for data modeling invariably assumes that an input/output partitioning of the data is a priori given. For linear models, this paradigm leads to computational problems of solving approximately overdetermined systems of linear equations. Examples of most simple data fitting problems, however, suggest that the a priori fixed input/output partitioning of the data may be inadequate: (1) the fitting criteria often depend implicitly on the choice of the input and output variables, which may be arbitrary, and (2) the resulting computational problems are ill-conditioned in certain cases. An alternative paradigm for data modeling, sometimes refered to as the behavioral paradigm, does not assume a priori fixed input/output partitioning of the data. The corresponding computational problems involve approximation of a matrix constructed from the data by another matrix of lower rank. The chapter proceeds with review of applications in systems and control, signal processing, computer algebra, chemometrics, psychometrics, machine learning, and computer vision that lead to low rank approximation problems. Finally, generic methods for solving low rank approximation problems are outlined. 2ff7e9595c
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