4. Linear Transformations and Matrix Algebra

Chapters (Interactive Linear Algebra):

• 3. Linear Transformations and Matrix Algebra
  • 3.1 Matrix Transformations
  • 3.2 One-to-one and Onto Transformations
  • 3.3 Linear Transformations
  • 3.4 Matrix Multiplication
  • 3.5 Matrix Inverses
  • 3.6 The Invertible Matrix Theorem

Videos:

• 3Blue1Brown: Linear transformations and matrices
• 3Blue1Brown: Matrix multiplication as composition
• 3Blue1Brown: Three-dimensional linear transformations
• 3Blue1Brown: The determinant
• 3Blue1Brown: Inverse matrices, column space and null space

• Khan Academy: Matrix transformations

• Exercises
  • Kimberly Brehm: Matrix Transformations
  • Kimberly Brehm: Introduction to Linear Transformations
  • Kimberly Brehm: Matrix Operations - Sums and Scalar Multiples
  • Kimberly Brehm: Matrix Operations - Multiplication and Transpose
  • Kimberly Brehm: The Inverse of a Matrix
  • Kimberly Brehm: Solving 2x2 Systems with the Inverse and Inverse Properties
  • Kimberly Brehm: Elementary Matrices And An Algorithm for Finding A Inverse
  • Kimberly Brehm: Characterizations of Invertible Matrices