Linear Algebra, Geometry and Transformation Textbooks in Mathematics Series
Auteur : Solomon Bruce
The Essentials of a First Linear Algebra Course and More
Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.
An Engaging Treatment of the Interplay among Algebra, Geometry, and Mappings
The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization.
A Smooth Transition to the Conceptual Realm of Higher Mathematics
This book guides students on a journey from computational mathematics to conceptual reasoning. It takes them from simple "identity verification" proofs to constructive and contrapositive arguments. It will prepare them for future studies in algebra, multivariable calculus, and the fields that use them.
Print Versions of this book also include access to the ebook version.
Vectors, Mappings, and Linearity. Solving Linear Systems. Linear Geometry. The Algebra of Matrices. Subspaces. Orthogonality. Linear Transformation. Appendices. Index.
Bruce Solomon is a professor in the Department of Mathematics at Indiana University Bloomington, where he often teaches linear algebra. He has held visiting positions at Stanford University and in Australia, France, and Israel. His research articles explore differential geometry and geometric variational problems. He earned a PhD from Princeton University.
Date de parution : 02-2015
17.8x25.4 cm
Thèmes de Linear Algebra, Geometry and Transformation :
Mots-clés :
Free Columns; Homogeneous Generators; First Linear Algebra Course; Standard Basis Vectors; Inverse Function And Rank Theorems; Solution Set; Geometric Treatment Of The Spectral Theorem; Scalar Multiplication; Linear Systems; Numeric Vector; Linear Vector Functions; Affine Subspace; GaussJordan Algorithm; Pivot Columns; Matrix/Vector Multiplication; Elementary Row Operations; Diagonalization; Independent Set; Orthogonality; Orthonormal Basis; Matrix Algebra; Non-zero Vector; Column Problem; Geometric Vectors; SVD Theorem; Augmented Matrix; Geometric Multiplicity; Geometric Duality; Algebraic Multiplicity; Characteristic Polynomial; Spectral Theorem; Reduced Row Echelon Form; Young Men; Orthogonally Diagonalizable; Entry-wise Multiplication