CS223 · Annotated SlidesChapter 2 — Matrix Operations
Chapter 2 · Annotated slides

Matrix Operations

Sums and scalar multiples, matrix multiplication as composition, the row–column rule, properties, powers and transposes.

Slide text Study notes Highlight: key words Tips, tricks & traps Seen again elsewhere How it can come up
Slide 1: CS 223: Computational Linear Algebra
Exam weight Low
    Slide 2: n columns
    Exam weight Low
      Slide 3: Sums and Scalar Multiples
      Exam weight Low
        Slide 4: Matrix Multiplication
        Exam weight High
        1. AB = [Ab₁ … Abₚ]; defined when A is m×n and B is n×p, giving m×p. (AB)ᵢⱼ = row i of A · column j of B.
        Exam trapAB ≠ BA in general; AB = AC does not imply B = C; AB = 0 does not imply A = 0 or B = 0.
        🎯 How this can come up · 1 question
        MCQ

        A is 3×2 and B is 2×4. AB is:

        Slide 5: Matrix Multiplication
        Exam weight Low
          Slide 6: Example
          Exam weight Low

            all

            Which means the whole matrix B

            Slide 7
            7
            Exam weight Low
              Slide 8: A is m × n B is n × p C is p × k
              Exam weight Low
                Slide 9: Slide 9
                Exam weight Low
                  Slide 10: Slide 10
                  Exam weight High
                  1. Transpose: (Aᵀ)ᵀ = A, (A + B)ᵀ = Aᵀ + Bᵀ, (AB)ᵀ = BᵀAᵀ (order reverses).
                  🎯 How this can come up · 1 question
                  MCQ

                  (AB)ᵀ equals:

                  Slide 11: Slide 11
                  Exam weight Low

                    Applications

                    1. Calculate A+B
                    2. Calculate C-D
                    3. Calculate A+C
                    4. Calculate A.B
                    5. Calculate 3A-5B 3
                    6. Calculate A
                    7. Calculate B. C T 2 + AB and compare the results
                    8. Calculate A(A + B) A and
                    Applications
                    12
                    Exam weight Low