CS223 · Chapter 2 · Annotated SlidesMatrix Operations
Original
Overview

Matrix Operations

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

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All 12 slides
  1. 1 CS 223: Computational Linear Algebra
  2. 2 n columns
  3. 3 Sums and Scalar Multiples
  4. 4 Matrix Multiplication
  5. 5 Matrix Multiplication
  6. 6 Example
  7. 7 Slide 7
  8. 8 A is m × n B is n × p C is p × k
  9. 9 Slide 9
  10. 10 Slide 10
  11. 11 Slide 11
  12. 12 Applications
Slide 1 / 12

CS 223: Computational Linear Algebra

Slide 1: CS 223: Computational Linear Algebra
Slide 2 / 12

n columns

Slide 2: n columns
Slide 3 / 12

Sums and Scalar Multiples

Slide 3: Sums and Scalar Multiples
Slide 4 / 12

Matrix Multiplication

Slide 4: Matrix Multiplication

Notes

  1. Trap AB ≠ BA in general; AB = AC does not imply B = C; AB = 0 does not imply A = 0 or B = 0.

Exam angle

PredictionQ1

A is 3×2 and B is 2×4. AB is:

Slide 5 / 12

Matrix Multiplication

Slide 5: Matrix Multiplication
Slide 6 / 12

Example

Slide 6: Example
Slide 7 / 12

Slide 7

Slide 7: Slide 7
Slide 8 / 12

A is m × n B is n × p C is p × k

Slide 8: A is m × n B is n × p C is p × k
Slide 9 / 12

Slide 9

Slide 9: Slide 9
Slide 10 / 12

Slide 10

Slide 10: Slide 10

Notes

  1. Transpose: (Aᵀ)ᵀ = A, (A + B)ᵀ = Aᵀ + Bᵀ, (AB)ᵀ = BᵀAᵀ (order reverses).

Exam angle

PredictionQ1

(AB)ᵀ equals:

Slide 11 / 12

Slide 11

Slide 11: Slide 11
Slide 12 / 12

Applications

Slide 12: Applications