During the Spring of 2005 I taught a course in intermediate linear algebra: a linear algebra course designed for students who have had a semester course in abstract algebra. It was taught seminar style: the students generated most of the proofs and presented their proofs in class. Consequently, it didn't cover as many topics as a lecture style course in linear algebra, but the students learned the material in greater depth.
LA1 (Jan 23, 2005). Review of rings and fields.
LA2 (Jan 30, 2005). Vector spaces.
LA3 (updated Feb 22, 2005). Subspaces. Spanning.
LA4 (Feb 1, 2005). Modules. Linear independence.
LA5 (Feb 13, 2005). Bases.
LA6 (Feb 22, 2005).
Basis size theorem. Dimension.
LA7 (Mar 1, 2005).
Linear maps. Module homomorphisms.
LA8 (Mar 6, 2005).
Kernel, image, isomorphisms.
LA9 (Mar 15, 2005).
Matrices. Hom spaces.
LA10 (Mar 15, 2005).
Dimension, rank, nullity.
LA11 (Mar 15, 2005).
Ring of matrices. Endomorphism ring.
LA12 (Mar 21, 2005).
Inverses. Row and Column manipulations.
LA13 (April 2, 2005).
Alternating bilinear functionals ("forms") and signed area.
LA14 (updated April 9, 2005).
Signed volume. Alternating n-linear functionals ("forms").
LA15 (updated April 12, 2005).
Alternating n-linear functionals: existence/uniqueness.
LA16 (updated April 12, 2005). Determinants.
LA17 (updated April 16, 2005). Cramer's Rule.
LA18 (updated April 16, 2005). Inverse Formula and unit determinant.
LA19 (April 14, 2005). Transpose. Cofactors. Column/Row Rank.
LA20 (updated April 19, 2005). Matrices for different bases.
Example 1 (April 23, 2005). Matrices for different bases.
FOR WED (April 27):
LA21 (updated April 19, 2005). Basis-dependent isomorphisms. Change of basis matrix.
Example 2 (April 23, 2005). Change of basis matrix.
LA22 (April 19, 2005). Homomorphisms of scalars. Similar matrices.
FOR MON (May 2):
LA23 (April 26, 2005). Eigenvalues and Eigenvectors.
FOR WED (May 4):
LA24 (May 2, 2005). Traces. Diagonalization.
LA25 (May 3, 2005). Existence of eigenvalues. Triangulating matrices.