Publisher's Synopsis
A Portrait of Linear Algebra provides students with a unified, elegant, modern, and comprehensive introduction to linear algebra that emphasizes the reading, understanding, and writing of proofs, while giving them advice on how to master these skills.Written in a student-friendly style, with precisely stated definitions and theorems, the NEW Third Edition of A Portrait of Linear Algebra by Jude Thaddeus Socrates:Features more than 500 additional exercises from the previous edition, including basic computations, assisted computations, true or false questions, mini-projects, and multi-step proofs broken down with hints for the student;Presents a thorough introduction to basic logic, set theory, axioms, theorems, and methods of proof;Gives an early introduction to the core concepts of spanning, linear independence, subspaces, basis, dimension, kernel, range, the fundamental matrix spaces and orthogonal complements.Integrates application topics from Physics, Chemistry, Differential Equations, Geometry, Computer Graphics, Group Theory, Recursive Sequences, and Number Theory.Includes topics not usually seen in an introductory book, such as the exponential of a matrix, the intersection of two subspaces, the pre-image of a subspace, cosets, quotient spaces, and the Isomorphism Theorems of Emmy Noether, a complete proof of Schur's Lemma and the Spectral Theorems, The Fundamental Theorem of Linear Algebra, the Singular Value Decomposition, and simultaneous diagonalization of commuting normal matrices, providing enough material for two full semesters.
