Elementary Linear Algebra
Systems of Linear Equations, Matrices, Vector Spaces, Linear Transformations, Applications.
Elementary Linear Algebra, Larson, Brooks/Cole, 8th edition.
1. Systems of linear equations; Gaussian elimination; matrices, matrix operations, properties, and inverses; and applications (including polynomial curve fittings, approximating integrals, network analysis, electrical circuits, chemical equations, input-output models) Sections 1.1-1.9.
2. Determinants, cofactor expansion, properties, Cramer's rule Sections 2.1-2.3.
3. Vectors in R2, R3, Rn, norm, dot-product, distance in Rn, orthogonality Sections 3.1-3.3.
4. Real vector spaces, subspaces, simple examples including spaces of functions and polynomials, spanning, linear independence, basis, dimension, change of basis, rank and nullity of a matrix, and properties of matrix transformations, applications. Sections 4.1-4.10.
5. **Eigenvalues and Eigenvectors, diagonalization, applications (e.g., Fibonacci type sequences). Sections 5.1-5.2.
8. Linear transformations, matrix representation, compositions, isomorphisms, inverses, similarity, dilations, reflections rotations, etc. Sections 8.1-8.5.
Orthogonal Bases: Gram-Schmidt Process. LU-Factorization, Fast Fourier Transform
*These and other topics at the instructor's discretion may be covered if time permits. ** Usually about one-third of the students are also enrolled in 220/221 and will need eigenvalues/eigenvectors.
(Porter 2016 )