Chapter LT  Linear Transformations

In the next linear algebra course you take, the first lecture might be a reminder about what a vector space is (Definition VS), their ten properties, basic theorems and then some examples. The second lecture would likely be all about linear transformations. While it may seem we have waited a long time to present what must be a central topic, in truth we have already been working with linear transformations for some time.

Functions are important objects in the study of calculus, but have been absent from this course until now (well, not really, it just seems that way). In your study of more advanced mathematics it is nearly impossible to escape the use of functions — they are as fundamental as sets are.

 Section LT Linear Transformations
  Subsection LT: Linear Transformations
  Subsection MLT: Matrices and Linear Transformations
  Subsection LTLC: Linear Transformations and Linear Combinations
  Subsection PI: Pre-Images
  Subsection NLTFO: New Linear Transformations From Old
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section ILT Injective Linear Transformations
  Subsection EILT: Examples of Injective Linear Transformations
  Subsection KLT: Kernel of a Linear Transformation
  Subsection ILTLI: Injective Linear Transformations and Linear Independence
  Subsection ILTD: Injective Linear Transformations and Dimension
  Subsection CILT: Composition of Injective Linear Transformations
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section SLT Surjective Linear Transformations
  Subsection ESLT: Examples of Surjective Linear Transformations
  Subsection RLT: Range of a Linear Transformation
  Subsection SSSLT: Spanning Sets and Surjective Linear Transformations
  Subsection SLTD: Surjective Linear Transformations and Dimension
  Subsection CSLT: Composition of Surjective Linear Transformations
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions
 Section IVLT Invertible Linear Transformations
  Subsection IVLT: Invertible Linear Transformations
  Subsection IV: Invertibility
  Subsection SI: Structure and Isomorphism
  Subsection RNLT: Rank and Nullity of a Linear Transformation
  Subsection SLELT: Systems of Linear Equations and Linear Transformations
  Subsection READ: Reading Questions
  Subsection EXC: Exercises
  Subsection SOL: Solutions