Linear Algebra
Spring 2014



Syllabus.
The course so far.
Record of assignments.
Solutions distributed in class.
The Greek alphabet.
Some tips on dealing with proofs.
Dot products and the Cauchy-Schwarz Inequality.
Cauchy-Schwarz and Triangle Inequalities (Calc III handout).
Proof of Theorem 1.13 (p. 54).
A proof that matrix multiplication is associative.
Some basic facts about inequalities.
Equivalence relations and partitions.
A proof of Lemma 2.7 (p118).
Classwork: Matrix mult and linear combinations.
p110#13b (ec problem).
Expressing solution sets using linear combinations.
Some consequences of the invariance of the Laplace expansion.
The cross product.
The proof of Theorem 3.7 [det(AB)=det(A)det(B)] (p66).
Classical adjoints and inverses.
One way in which section 3.4 can be applied.
Classwork on eigenvalues and eigenspaces.
Definition of vector space and a page from your calculus text.
The first theorem about abstract vector spaces.
An expanded version of Theorem 4.5 (p. 250).
From "dependent" to "independendent" via MAT 225.
A useful test for linear dependence/independence.
Why the r.r.e.f. is unique.
Some characterizations of linear dependence/independence.
A proof of Theorem 3. 7 [det(AB)=det(A)det(B)]using elementary matrices.
A program to compute determinant by row reduction.
Extra Credit Project (formula for Fibonacci numbers).
Proof of Lemma 4.11 (slightly reworked).
A proof that rref is unique.
The transition matrix between two coordinatizations.
The matrix of a rotation in the plane.
Proof of Theorem 5.8 and explanation why matrix mult. is associative.
A good chapter on induction (from a discrete math text).