000			02581nam a22002297a 4500
003			IIITD
005			20240504104120.0
008			240412b |||||||| |||| 00| 0 eng d
020			_a9783030528140
040			_aIIITD
082			_a512.5 _bJOH-A
100			_aJohnston, Nathaniel
245			_aAdvanced linear and matrix algebra _cby Nathaniel Johnston.
260			_aSwitzerland : _bSpringer, _c©2021
300			_axvi, 494 p. : _bcol. ill. ; _c23 cm.
504			_aIncludes bibliographical references and index.
505			_tChapter 1: Vector Spaces _tChapter 2: Matrix Decompositions _t Chapter 3: Tensors and Multilinearity _tAppendix A: Mathematical Preliminaries _tAppendix B: Additional Proofs _t Appendix C: Selected Exercise Solutions.
520			_aThis textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, Introduction to Linear and Matrix Algebra.
650			_a Algebra
650			_a Linear Algebra
942			_2ddc _cBK
999			_c172455 _d172455