Advanced Linear and Matrix Algebra Johnston Nathaniel
Advanced Linear and Matrix Algebra Johnston Nathaniel This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Building on a…
Specifikacia Advanced Linear and Matrix Algebra Johnston Nathaniel
Advanced Linear and Matrix Algebra Johnston Nathaniel
This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book.
Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. 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. In each case, the author ties the new technique back to familiar ones, to
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