A01=Donald S Passman
Adjoint Matrix
Author_Donald S Passman
Axiom of Choice
Basis
Bilinear Form
Category=PBF
Cauchy-Schwarz Inequality
Cayley-Hamilton Theorem
Characteristic Polynomial
Cofactor Expansion
Companion Matrix
Congruent Matrices
Cramer's Rule
Determinant
Dimension
Dual Basis
Dual Space
Eigenvalue
Eigenvector
Elementary Matrix
Elementary Row Operation
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Field
Gaussian Elimination
Gram-Schmidt Method
Hermitian Bilinear Form
Hilbert Matrix
Image
Jordan Canonical Form
Kernel
Linear Equation
Linear Transformation
Linearly Independent
Matrix
Matrix Addition
Matrix Multiplication
Maximal Linearly Independent Set
Minimal Polynomial
Minimal Spanning Set
Nilpotent Transformation
Nonsingular
One-to-One Function
Onto Function
Orthonormal Basis
Parallelogram Law
Quadratic Form
Quotient Space
Rank
Reduced Row Echelon Form
Replacement Theorem
Ring of Matrices
Row Echelon Form
Schroeder-Bernstein Theorem
Similar Matrices
Solution Space
Spanning Set
Square Matrix
Sylvester's Law of Inertia
System of Linear Equations
Trace
Triangle Inequality
Vandermonde Matrix
Vector
Vector Space
Volume Function
Well-Ordering Principle
Zorn's Lemma
Product details
- ISBN 9789811254840
- Publication Date: 07 Apr 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book consists of the expanded notes from an upper level linear algebra course given some years ago by the author. Each section, or lecture, covers about a week's worth of material and includes a full set of exercises of interest. It should feel like a very readable series of lectures. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and uses those axioms to define and explain vector spaces. Then he carefully explores the relationship between linear transformations and matrices. Determinants are introduced as volume functions and as a way to determine whether vectors are linearly independent. Also included is a full chapter on bilinear forms and a brief chapter on infinite dimensional spaces.The book is very well written, with numerous examples and exercises. It includes proofs and techniques that the author has developed over the years to make the material easier to understand and to compute.
