Linear Algebra: Table of Contents

Lecture 1: What is Linear Algebra?

Lecture 2: Gaussian Elimination

Section 2.1: Notation for Linear Systems

Section 2.2: Reduced Row Echelon Form

Lecture 3: Elementary Row Operations

Lecture 4: Solution Sets for Systems of Linear Equations

Section 4.1: Non-Leading Variables

Lecture 5: Vectors in Space, n-Vectors

Section 5.1: Directions and Magnitudes

Lecture 6: Vector Spaces

Lecture 7: Linear Transformations

Lecture 8: Matrices

Lecture 9: Properties of Matrices

Section 9.1: Block Matrices

Section 9.2: The Algebra of Square Matrices

Lecture 10: Inverse Matrix

Section 10.1: Three Properties of the Inverse

Section 10.2: Finding Inverses

Section 10.3: Linear Systems and Inverses

Section 10.4: Homogeneous Systems

Section 10.5: Bit Matrices

Lecture 11: LU Decomposition

Section 11.1: Using LU Decomposition to Solve Linear Systems

Section 11.2: Finding an LU Decomposition

Section 11.3: Block LU Decomposition

Lecture 12: Elementary Matrices and Determinants

Section 12.1: Permutations

Section 12.2: Elementary Matrices

Lecture 13: Elementary Matrices and Determinants II

Lecture 14: Properties of the Determinant

Section 14.1: Determinant of the Inverse

Section 14.2: Adjoint of a Matrix

Section 14.3: Application: Volume of a Parallelepiped

Lecture 15: Subspaces and Spanning Sets

Section 15.1: Subspaces

Section 15.2: Building Subspaces

Lecture 16: Linear Independence

Lecture 17: Basis and Dimension

Section 17.1: Bases in Rⁿ

Lecture 18: Eigenvalues and Eigenvectors

Section 18.1: Invariant Directions

Lecture 19: Eigenvalues and Eigenvectors II

Section 19.1: Eigenspaces

Lecture 20: Diagonalization

Section 20.1: Matrix of a Linear Transformation

Section 20.2: Diagonalization

Section 20.3: Change of Basis

Lecture 21: Orthonormal Bases

Section 21.1: Relating Orthonormal Bases

Lecture 22: Gram-Schmidt and Orthogonal Complements

Section 22.1: Orthogonal Complements

Lecture 23: Diagonalizing Symmetric Matrices

Lecture 24: Kernel, Range, Nullity, Rank

Section 24.1: Summary

Table of Contents