Summary
Linear algebra, or Modern Algebra, is algebra with vector values – i.e. more than one parameter – in place of scalar values like numbers, which have a single scalar parameter.
Course Outline
- I. Introduction to Linear Algebra
- A. Overview of the course
- B. Importance of linear algebra in mathematics and other fields
- C. Course goals and objectives
- II. Vectors
- A. Definition of vectors
- B. Types of vectors (column, row, and spatial)
- C. Vector arithmetic (addition, subtraction, scalar multiplication)
- D. Dot product and cross product
- III. Matrices
- A. Definition of matrices
- B. Matrix operations (addition, subtraction, scalar multiplication)
- C. Matrix-vector multiplication
- D. Matrix-matrix multiplication
- E. Inverse of a matrix
- IV. Systems of Linear Equations
- A. Definition of systems of linear equations
- B. Representation of systems of linear equations using matrices
- C. Gaussian elimination and Gauss-Jordan elimination
- D. LU Decomposition
- E. Matrix inverse method
- V. Eigenvalues and Eigenvectors
- A. Definition of eigenvalues and eigenvectors
- B. Calculation of eigenvalues and eigenvectors
- C. Properties of eigenvalues and eigenvectors
- D. Applications of eigenvalues and eigenvectors
- VI. Orthogonality and Orthogonal Projections
- A. Definition of orthogonality
- B. Orthogonal projections
- C. Orthogonal matrices
- D. Orthonormal basis
- VII. Determinants
- A. Definition of determinants
- B. Calculation of determinants
- C. Properties of determinants
- D. Applications of determinants
- VIII. Conclusion
- A. Summary of key concepts and results
- B. Final thoughts and future directions
- C. Review of course goals and objectives
- IX. Final Exam
- A. Comprehensive assessment of course material
- B. Written and/or practical components
- C. Grading and evaluation criteria