Linear Algebra 2

Office Hours

• Wed 6:30pm - 7:30pm
• Fri 5:30pm - 6:30pm

Schedule

Notes

• All quizes based off homeworks
• Best 4/5 quizzes
• Quizzes start from week 3 in tutorial
• All computations should have whole numbers or Complex Number, but they should be easy
• 30% (4-6hrs per week) understanding basic defn, terms, computations. This is the most important
• 60% (1-2hrs per week) understanding problems from class and most homeworks
• 80% (1-2hrs per week) understanding what is presented
• Late submission policy after 4 days

Concepts

Week 0.1

• Field
• Integer Modulo n
• Congruent Modulo
• Equivalence
  • Reflexive
  • Symmetric
  • Transitive
• Modulus
• Uniqueness Field Properties

Week 1.1

• Ring
• Commutative Rings
• Integral Domain
• Principle Ideal Domain
• Euclidean Domain
• Additive Subgroup
• Ideal
• Field

Week 1.2

• Generator for Ideal
• Euclidean Algorithm (GCD)
• Remainder Theorem
• Polynomial Ideal
• Vector Space
• Linear Combination
• Span
• Linear Independence
• Basis

Week 2

• Vector Space
• Subspace
• Spanning Set
• Linear Independence

Week 3

• Swap Operator
• Permutation Notation
• Standard Basis Matrix
• Vector Space Isomorphic
• Ordered Basis
• Linear Operator

Week 4

• Change of Basis
• Linear Functional
• Orthogonal Set
• Standard Inner Product
  • Standard Inner Product for Complex Numbers
  • Standard Inner Product for Real Numbers
  • Standard Inner Product Function
• Riesz Representation Theorem
• Annihilator
• Error Correcting Codes

Week 5

• XOR Encryption
• Metric
• Norm
• Norm Function