Linear algebra is the study of vectors and linear transformations. This text is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.
- 1: What is Linear Algebra?
- 2: Systems of Linear Equations
- 3: The Simplex Method
- 4: Vectors in Space, n-Vectors
- 5: Vector Spaces
- 6: Linear Transformations
- 7: Matrices
- 8: Determinants
- 9: Subspaces and Spanning Sets
- 10: Linear Independence
- 11: Basis and Dimension
- 12: Eigenvalues and Eigenvectors
- 13: Diagonalization
- 14: Orthonormal Bases and Complements
- 15: Diagonalizing Symmetric Matrices
- 16: Kernel, Range, Nullity, Rank
- 17: Least Squares and Singular Values
- Appendices: Symbols, Fields, Sample Exams, Online Resources, Movie Scripts Edit section
Thumbnail: 3 planes intersect at a point. Image used with permission (CC BY-SA 4.0; Fred the Oyster).