Linear Algebra B (Maths 159)

Lecturer: Dr. Theodore Voronov (MSS/P5)

• Syllabus

Lecture notes

• Lecture 1. Real vector spaces: revision
• Lecture 2. Linear transformations
• Lecture 3. Inverse linear transformations. Isomorphisms of vector spaces
• Lecture 4. Matrices of linear transformations
• Lecture 5. Matrix of composition. Changes of bases. Similarity of matrices
• Lecture 6. Scalar products
• Lecture 7. Properties of Euclidean spaces
• Lecture 8. Gram-Schmidt orthogonalization process. Orthogonal matrices
• Lecture 9. Orthogonal matrices and orthogonal operators
• Lecture 10. Self-adjoint operators and symmetric matrices
• Lecture 11. Bilinear and quadratic forms

Exercises

• Exercises 1. Linear Transformations
  Solutions
• Exercises 2. Matrices of linear transformations
  Solutions
• Exercises 3. Scalar products
  Solutions
• Exercises 4. Diagonalization of symmetric matrices
  Solutions
• Exercises 5. Quadratic forms
  Solutions