Week 1: Vectors and vector spaces
Week 2:Linear maps I: Definition, Spaces associated with a map, Matrices
Week 3: Linear maps II: Invertible linear maps, Elementary row/column operations, Solving linear equations, Quotient space
Week 4: Linear maps III: Four fundamental spaces, Rank of a matrix, Determinants, Change of basis
Week 5:Eigenvalues and eigenvectors of linear operators
Week 6: Applications of eigenvalues
Week 7: Inner product spaces
Week 8:Projection and least squares
Week 9:Adjoint of linear maps and operators
Week 10:Self-adjoint and normal operators
Week 11: Positive operators, isometries
Week 12:Polar and singular value decompositions
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