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Linear Transformations - Overview

Introduction​

High-level overview of linear transformations, their properties, and relationship to matrices.

Key Concepts​

Definition​

  • What is a linear transformation?
  • Linearity properties: T(u + v) = T(u) + T(v) and T(cv) = cT(v)

Matrix Representation​

  • Every linear transformation can be represented as a matrix
  • Change of basis

Kernel and Image​

  • Kernel (null space) of T
  • Image (range) of T
  • Rank-nullity theorem

Special Transformations​

  • Projections
  • Rotations
  • Reflections

Applications​

  • Computer graphics
  • Data transformations
  • Function spaces

References​