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[null,"1.","Record Nr.",null,"UNINA9910337642503321"]
[null,null,"Autore",null,"Martínez-Guerra Rafael"]
[null,null,"Titolo",null,"Algebraic and Differential Methods for Nonlinear Control Theory : Elements of Commutative Algebra and Algebraic Geometry / / by Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019"]
[null,null,"ISBN",null,"3-030-12025-2"]
[null,null,"Edizione",null,"[1st ed. 2019.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XIV, 196 p. 13 illus., 11 illus. in color.)"]
[null,null,"Collana",null,"Mathematical and Analytical Techniques with Applications to Engineering, , 1559-7466"]
[null,null,"Disciplina",null,"620.00151"]
[{"$nulls":4},"629.836"]
[null,null,"Soggetti",null,"Engineering mathematics"]
[{"$nulls":4},"Nonlinear Optics"]
[{"$nulls":4},"Control engineering"]
[{"$nulls":4},"System theory"]
[{"$nulls":4},"Control theory"]
[{"$nulls":4},"Engineering Mathematics"]
[{"$nulls":4},"Control and Systems Theory"]
[{"$nulls":4},"Systems Theory, Control"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Mathematical Background -- Group Theory -- Rings -- Matrices and linear equations systems -- Permutations and Determinants -- Vector and Euclidean Spaces -- Linear Transformations -- Matrix Diagonalization and Jordan Canonical Form -- Differential Equations -- Differential Algebra for Nonlinear Control Theory -- Appendix -- Index."]
[null,null,null,"Sommario/riassunto","This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the "]
[{"$nulls":4},"ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra."]