==== Unit: Matrices and Vectors =====


=== Matrix Manipulations (45 minutes)===

  * [[..:prereq:prpre:prprematrix|Prerequisite Ideas]]
  * [[..:lecture:prlec:prlecmatrixmanip|Review of matrix manipulations]] (Lecture, 45 minutes)
  * [[..:hw:prhw:prhwmatrix|Homework]]



=== Introduction to Bra-ket notation (15 minutes)===

  * [[..:prereq:prpre:prprebraket|Prerequisite Ideas]]
  * [[..:lecture:prlec:prlecbraket|Introduction to bra-ket notation]] (Lecture, ?? minutes)   - FIXME Emphasize normalization and finding components.  Add a good SWBQ or small group activity.
  * [[..:hw:prhw:prhwbraket|Homework]]



==== Unit: Operators and Transformations in Linear Systems ====


=== Linear Transformations (1 1/2 hr)===

  * [[..:prereq:prpre:prprelintran|Prerequisite Ideas]]
  * [[..:activities:pract:prlineartrans|Linear Transformations Activity]] (Small Group Activity) 
  * [[..:hw:prhw:prhwlintran|Homework]]


=== Tangible Metaphor for Complex Vectors (10 minutes)===

  * [[..:activities:pract:prcomplexarms|Visualizing Complex Two Component Vectors]] (Kinesthetic Activity)

=== Properties of Linear Vector Spaces (30 min)===

  * [[..:prereq:prpre:prprehermmat|Prerequisite Ideas]]
  * [[..:lecture:prlec:prlecvectorspaces|Properties of linear vector spaces]] (Optional Lecture, ?? minutes)


=== Inner Products and Norms ===

  * Calculating Inner Products and Normalization of Vectors (Lecture, ?? minutes)

FIXME  Write these lecture notes.  Emphasize complex vectors.

=== Matrix Components (40 min) ===

  * [[..:prereq:prpre:prprerotmatr|Prerequisite Ideas]]
  * [[..:activities:pract:prmatrixelems|Finding Matrix Elements]] (Small Group Activity) FIXME Work in comments about Fourier series into wrap-up.
  * [[..:hw:prhw:prhwcomponents|Homework]]



=== Rotation Matrices in 2 and 3 Dimensions (10 min)===

  * [[..:prereq:prpre:prprerotmatr|Prerequisite Ideas]]
  * [[..:lecture:prlec:prlecrotations|Rotation Matrices in 2 and 3 Dimensions]]  (Lecture, ?? minutes).
  * [[..:hw:prhw:prhwrotmatr|Homework]]

==== Unit: Eigenvalues and Eigenvectors =====


=== Eigenvalues & Eigenvectors (2 hr)===

  * [[..:prereq:prpre:prpreeigenv|Prerequisite Ideas]]
  * [[..:lecture:prlec:prleceigenvalues|Method for finding eigenvalues and eigenvectors for 2x2 and 3x3 matrices]] (Lecture)
  * [[..:activities:pract:preigenvectors|Eigenvectors and Eigenvalues Activity]] (Small Group Activity)
  * [[..:hw:prhw:prhweigenv|Homework]]


=== Special Properties of Hermitian Matrices (40 min)===

  * [[..:prereq:preface:prehermitian|Prerequisite Ideas]]
  * [[..:lecture:prlec:prlechermitian|Properties of Hermitian matrices]]  (Lecture, ?? minutes)
  * [[..:lecture:prlec:prlecdiagonal|Diagonalization of matrices]]  (Lecture, ?? minutes)
  * [[..:activities:pract:prdiagmatrix|Diagonalizing Matrices]] (Small Group Activity).
  * [[..:hw:prhw:prhwdiagonal|Homework]]


=== Commuting Matrices (10 min)===

  * [[..:lecture:prlec:prleccommute|Properties of commuting matrices]]  (Lecture, ?? minutes)
  * [[..:hw:prhw:prhwcommute|Homework]]
  
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