Elementary Linear Algebra – Ron Larson, David C. Falvo – 6th Edition

1. Systems of Linear Equations.
Introduction to Systems of Linear Equations. Gaussian Elimination and Gauss-Jordan Elimination. pplications of Systems of Linear Equations.
2. Matrices.
Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Applications of Matrix Operations.
3. Determinants.
The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Introduction to Eigenvalues. Applications of Determinants.
4. Vector Spaces.
Vectors in R”. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces.
5. Inner Product Spaces.
Length and Dot Product in R”. Inner Product Spaces. Orthonormal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces.
6. Linear Transformations.
Introduction to Linear Transformations. The Kernel and Range of a Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations.
7. Eigenvalues and Eigenvectors.
Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors.
8. Complex Vector Spaces (Online).
Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and DeMoivre’s Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Matricies.