Systems of Linear Equations. Row Operations
Row Reduction and Echelon Forms
Solutions Sets of Linear Systems
Key Ideas in Chapter 1: Linear Equations and Chapter 3: Linear Transformations
Characterizations of Invertible Matrices
Cramer`s rule, Volume and Linear Transformation
Linearly Independence Sets. Bases.
The Dimension of a Vector Space.
Complex Vector Spaces. Complex Eigenvalues.
Inner Product, Length, and Orthogonality
Orthogonal Complements Theorem
Orthogonal Sets. Orthogonal Projections
Least-Squares Problems. Application to Linear Models
Diagonalization of Symmetric Matrices