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Application-inspired linear algebra

Moon, Heather A.

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Application-inspired linear algebra

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Application-inspired linear algebra/ by Heather A. Moon, Thomas J. Asaki, Marie A. Snipes.
作者:	Moon, Heather A.
其他作者:	Asaki, Thomas J.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xxi, 528 p. :ill. (some col.), digital ;24 cm.
內容註:	1 Introduction -- 2 Vector Spaces -- 3 Vector Space Arithmetic and Representations -- 4 Linear Transformations -- 5 Invertibility -- 6 Diagonalization -- 7 Inner Product Spaces and Pseudo-Invertibility -- 8 Conclusions -- A Radiography and Tomography -- B The Diffusion Equation -- C Proof Techniques -- D Fields.
Contained By:	Springer Nature eBook
標題:	Algebras, Linear. -
電子資源:	https://doi.org/10.1007/978-3-030-86155-1
ISBN:	9783030861551

Application-inspired linear algebra
Moon, Heather A.

Application-inspired linear algebra[electronic resource] /by Heather A. Moon, Thomas J. Asaki, Marie A. Snipes. - Cham :Springer International Publishing :2022. - xxi, 528 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate texts in mathematics and technology,1867-5514. - Springer undergraduate texts in mathematics and technology..

1 Introduction -- 2 Vector Spaces -- 3 Vector Space Arithmetic and Representations -- 4 Linear Transformations -- 5 Invertibility -- 6 Diagonalization -- 7 Inner Product Spaces and Pseudo-Invertibility -- 8 Conclusions -- A Radiography and Tomography -- B The Diffusion Equation -- C Proof Techniques -- D Fields.

This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, one of which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors' website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.

ISBN: 9783030861551

Standard No.: 10.1007/978-3-030-86155-1doiSubjects--Topical Terms:

521915
Algebras, Linear.

LC Class. No.: QA184.2 / .M66 2022

Dewey Class. No.: 512.5

Application-inspired linear algebra
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505 0 $a 1 Introduction -- 2 Vector Spaces -- 3 Vector Space Arithmetic and Representations -- 4 Linear Transformations -- 5 Invertibility -- 6 Diagonalization -- 7 Inner Product Spaces and Pseudo-Invertibility -- 8 Conclusions -- A Radiography and Tomography -- B The Diffusion Equation -- C Proof Techniques -- D Fields.
520 $a This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, one of which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors' website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
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