Chapter Three: Maps Between Spaces

Isomorphisms

• DefinitionAndExamples
  • Exercises Three I 1
• DimensionCharacterizesIsomorphism
  • Exercises Three I 2

Homomorphisms

• Definition
  • Exercises Three II 1
• RangespaceAndNullspace
  • Exercises Three II 2

ComputingLinearMaps

• RepresentingLinearMapsWithMatrices
  • Exercises Three III 1
• AnyMatrixRepresentsALinearMap
  • Exercises Three III 2

MatrixOperations

• SumsAndScalarProducts
  • Exercises Three IV 1
• MatrixMultiplication
  • Exercises Three IV 2
• MechanicsOfMatrixMultiplication
  • Exercises Three IV 3
• Inverses
  • Exercises Three IV 4

ChangeOfBasis

• ChangingRepresentationsOfVectors
  • Exercises Three V 1
• ChangingMapRepresentations
  • Exercises Three V 2

Projection

• OrthogonalProjectionIntoALine
  • Exercises Three VI 1
• GramSchmidtOrthogonalization
  • Exercises Three VI 2
• ProjectionIntoASubspace
  • Exercises Three VI 3

Topics

• LineOfBestFit
  • Exercises Three VII 1
• GeometryOfLinearMaps
  • Exercises Three VII 2
• MarkovChains
  • Exercises Three VII 3
• OrthonormalMatrices
  • Exercises Three VII 4

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