Bogacki P. Linear Algebra: Concepts and Applications

Washington: MAA Press, 2019. — 397 p.This is a textbook designed for an introductory linear algebra course. While many students may have been exposed to some of the relevant topics (e.g., vectors, matrices, determinants, etc.) it is the author’s experience that no such familiarity can be assumed of all students; consequently, this book assumes none.Glossary of Notation
Vectors and Matrices
Vectors
Matrices
Matrix Multiplication
Introduction to Linear Transformations
Chapter Review
Linear Systems
Systems of Linear Equations
Elementary Matrices and the Geometry of Linear Systems
Matrix Inverse
Applications of Linear Systems and Matrix Factorizations
Chapter Review
Determinants
Cofactor Expansions
Applications of Determinants
Chapter Review
Vector Spaces
Vector Spaces
Subspaces
Linear Independence
Basis and Dimension
Coordinates
Rank and Nullity
Chapter Review
Linear Transformations
Linear Transformations in General Vector Spaces
Kernel and Range
Matrices of Linear Transformations
Chapter Review
Orthogonality and Projections
Orthogonality
Orthogonal Projections and Orthogonal Complements
Gram-Schmidt Process and Least Squares Approximation
Introduction to Singular Value Decomposition
Chapter Review
Eigenvalues and Singular Values
Eigenvalues and Eigenvectors
Diagonalization
Applications of Eigenvalues and Eigenvectors
Singular Value Decomposition
Chapter Review
Answers to Selected Odd-Numbered Exercises
Recurring References to Selected Transformations in R
Twelve Equivalent Statements